<JSP>
{ Taala-JSP CODE FOR JSX CONVERSION 28.11.2019 MEP }
{ Muista täpättää LaTeX points: }

{ Lineaarialgebra: PNS-ratkaisu 3x2 2D-3D visualisointi }

{ JSX board name: PNSratkaisu3x2 }
{ JSX element id: pnsratkaisu3x2 }

#CODE     = "GSP.class"
#CODEBASE = "../jsp"
#ARCHIVE  = "jsp4.jar"
#WIDTH    = 800
#HEIGHT   = 430
#ALIGN    = Center
*Frame          =   1
*TextFont       =   "Courier"
*TextBold       =   0
*TextSize       =  14
*LabelFont      =   "Courier"
*LabelBold      =   0
*LabelSize      =  14
*MeasureFont        =   "Courier"
*MeasureSize        =  12
*MeasureBold        =   0
*MeasureInDegrees   =   1
*DirectedAngles     =   0
*Backblue       = 255
*BackGreen      = 255
*Backred        = 255

${
$x1T	FixedText(410, 360,'x1')[ plain, font('Helvetica'), bold,     red, justifyCenter];
$x2T	FixedText(765, 300,'x2')[ plain, font('Helvetica'), bold,    blue, justifyCenter];
$x3T   	FixedText(588,  10,'x3')[ plain, font('Helvetica'), bold,   color(0,150,0), justifyCenter];
$}

${ Dividing vertical segment
$UpperPt2 	FixedPoint(750, 20)[hidden];
$LowerPt2 	FixedPoint(750,520)[hidden];
$VLine2 	Segment($UpperPt2,$LowerPt2)[black,thick];
$}

{ Dividing vertical segment ib the middle }
$UpperPt 	FixedPoint(400,50)[hidden];
$LowerPt 	FixedPoint(400,430)[hidden];
$VLine 		Segment($UpperPt,$LowerPt)[black,thick];


$AText	FixedText(65,  34, 'A')[black,bold,justifyCenter];
{,text('\\( A \\)')}
$xText	FixedText(165,  40, 'x')[black,bold,justifyCenter];
{,text('\\( \\mathbf{x}\\)')}
$AxText	FixedText(260,  34, 'Ax = b''')[black,bold,justifyCenter,hidden];
{,text('\\( A\\mathbf{x} = \\mathbf{b}'' \\)')}
$x1Text	FixedText(160,  60, 'x1')[black,bold,justifyCenter];
{,text('\\( xSUB{1} \\)')}
$x2Text	FixedText(160,  80, 'x2')[black,bold,justifyCenter];
{,text('\\( xSUB{2} \\)')}
$eqsign	FixedText(135,  65, '=')[black,bold,justifyCenter];
$bText	FixedText(270,  34, 'b')[black,bold,justifyCenter];
{,text('\\( \\mathbf{b}\\)')}

{ Lähtötaso R2 }
$OrigoR2 FixedPoint(200,200)[black, bold, label('0')];
$xykkR2   UnitPoint($OrigoR2, 50)[white, bold, label('1'),hidden];
$xykkR2seen   Translation($xykkR2, 0,0)[plain, white, bold, label('1')];
$coord  Origin&Unit($OrigoR2,$xykkR2)[hidden];

$XaxR2    AxisX($coord)[black,hidden];
$YaxR2    AxisY($coord)[black,hidden];

$LEx	FixedPoint(  5,200)[hidden];
$REx	FixedPoint(395,200)[hidden];
$XaxVis	Segment($LEx,$REx)[black];
{,arrowL}
$UEy	FixedPoint(200,85)[hidden];
$LEy	FixedPoint(200,370)[hidden];
$YaxVis	Segment($LEy,$UEy)[black];
{,arrowL}

$yykkR2	Translation($OrigoR2,0,50)[plain, white, bold, label('1')];
$x1x2	Point(300,100)[red,label('x')];
{,label('\\mathbf{x}'),LabelAlign(5,5),highlight}
$SOx1x2	Segment($OrigoR2,$x1x2)[magenta];
{,arrowL}

$x1Parx2 Parallel($YaxR2,$x1x2)[blue,hidden];	
$Rptx1	Intersect($XaxR2,$x1Parx2)[black, label('x1')];
{,label('xSUB{1}'),LabelAlign(5,5)}
$Sx1x2x1 Segment($x1x2,$Rptx1)[blue];
{,dash(2)}
$x1	Ratio/Points($OrigoR2,$xykkR2,$Rptx1,45,120,'')[black];
$x1text FixedText(80,125, 'x1 = ')[black];
{,text('\\( xSUB{1} \\ = \\)' )}
$x2Parx2 Parallel($XaxR2,$x1x2)[red,hidden];	
$Rptx2	Intersect($YaxR2,$x2Parx2)[black, label('x2')];
{,label('xSUB{2}'),LabelAlign(5,5)}
$Sx1x2x2 Segment($x1x2,$Rptx2)[red];
{,dash(2)}
$x2	Ratio/Points($OrigoR2,$yykkR2,$Rptx2,45,140,'')[black];
$x2text FixedText(80,145, 'x2 = ')[black];
{,text('\\( xSUB{2} \\ = \\)' )}

{ The real lines for A columns }
$LUpp	FixedPoint(0,370)[hidden];
$LLow	FixedPoint(0,430)[hidden];
$RLow	FixedPoint(400,430)[hidden];
$RUpp	FixedPoint(400,370)[hidden];
$ULine	Line($LUpp,$RUpp)[black, hidden];
$RectA	Polygon($LUpp,$LLow,$RLow,$RUpp,$LUpp)[yellow, hidden];

$ROa1	FixedPoint(200,390)[black,label('0'), hidden];
{,labelAlign(-3,6)}
$Refa1	Translation($ROa1,25,0)[hidden];
$Raya1	Ray($Refa1,$ROa1)[black, hidden];
$Rykka1	Point on object($Raya1,1)[white, label('1'), hidden];
$R1a1	FixedPoint(225,390)[white,label('1'), hidden];
{,labelAlign(-3,6)}
$RLa1	Line($Rykka1,$ROa1)[black, hidden];
$LE1	FixedPoint(0,390)[hidden];
$RE1	FixedPoint(400,390)[hidden];
$SRLa1	Segment($LE1,$RE1)[black,hidden];
{,arrowL}

$ROa2	FixedPoint(200,415)[black,label('0'), hidden];
{,labelAlign(-4,-12)}
$Refa2	Translation($ROa2,25,0)[hidden];
$Raya2	Ray($Refa2,$ROa2)[black, hidden];
$Rykka2	Point on object($Raya2,1)[white, label('1'), hidden];
$R1a2	FixedPoint(225,415)[white,label('1'), hidden];
{,labelAlign(-4,-12)}
$RLa2	Line($Rykka2,$ROa2)[black, hidden];

$LE2	FixedPoint(0,415)[hidden];
$RE2	FixedPoint(400,415)[hidden];
$SRLa2	Segment($LE2,$RE2)[black,hidden];
{,arrowL}

${
The real b line

$LbUpp	FixedPoint(772,0)[hidden];
$LbLow	FixedPoint(772,386)[hidden];
$RbLow	FixedPoint(806,386)[hidden];
$RbUpp	FixedPoint(806,0)[hidden];
$UbLine	Line($LUpp,$RUpp)[black, hidden];
$Rectb	Polygon($LbUpp,$LbLow,$RbLow,$RbUpp,$LbUpp)[color(200,240,200), hidden];

$ROb	FixedPoint(780,200)[black,label('0'), hidden];
$Refb	Translation($ROb,0,25)[hidden];
$Rayb	Ray($Refb,$ROb)[black, hidden];
$Rykkb	Point on object($Rayb,1)[white, label('1'), hidden];
$R1b	FixedPoint(780,175)[white,label('1'), hidden];
$RLb	Line($Rykkb,$ROb)[black, hidden];

$bUp	FixedPoint(780,0)[hidden];
$bLo	FixedPoint(780,385)[hidden];
$SLb	Segment($bUp,$bLo)[black,hidden];

$Rptb1	Point on object($RLb,-4)[label('b1'), red, layer(10), hidden];
{,label('bSUB{1}'),LabelAlign(5,5),highlight}
$b1	Ratio/Points($ROb,$Rykkb,$Rptb1,205,50,'')[red];

$Rptb2	Point on object($RLb,4)[label('b2'), blue, layer(10), hidden];
{,label('bSUB{2}'),LabelAlign(5,5),highlight}
$b2	Ratio/Points($ROb,$Rykkb,$Rptb2,205,65,'')[blue];

$Rptb3	Point on object($RLb,2)[label('b3'), color(0,150,0), layer(10), hidden];
{,label('bSUB{3}'),LabelAlign(5,5),highlight}
$b3	Ratio/Points($ROb,$Rykkb,$Rptb3,205,80,'')[color(0,150,0)];
$}

{ The virtual 3-space }
$OrigoR3	FixedPoint(600,210)[black,  label('0')];
$xykkRef	Point(580,220)[red,  hidden];
$yykkRef	Point(625,215)[blue, hidden];
$zykkRef	Point(600,190)[green,hidden];

$xRay	Ray($xykkRef,$OrigoR3)[ hidden];
$xykk	Point on object( $xRay,1)[ white, label('1')];
$xRL	Line($xykk,$OrigoR3)[ red,hidden];
$yRay	Ray($yykkRef,$OrigoR3)[ hidden];
$yykk	Point on object( $yRay,1)[ white, label('1')];
$yRL	Line($yykk,$OrigoR3)[ blue,hidden];
$zRay	Ray($zykkRef,$OrigoR3)[ hidden];
$zykk	Point on object( $zRay,1)[ white, label('1')];
$zRL	Line($zykk,$OrigoR3)[color(0,150,0),hidden];
$zUp	FixedPoint(600,0)[hidden];
$zLo	FixedPoint(600,385)[hidden];
$zvisib Segment($zUp,$zLo)[color(0,150,0),hidden];


$xM		Point on object($xRL,-8)[red,hidden];
$xP		Point on object($xRL, 8)[red,hidden];

$xRLvis		Segment($xM,$xP)[red];
{,arrowL}

$yM		Point on object($yRL,-7)[blue,hidden];
$yP		Point on object($yRL, 7)[blue,hidden];

$yRLvis		Segment($yM,$yP)[blue];
{,arrowL}
$zM		Point on object($zRL,-10)[color(0,150,0),hidden];
$zP		Point on object($zRL, 10)[color(0,150,0),hidden];

$zRLvis		Segment($zM,$zP)[color(0,150,0)];
{,arrowL}
$xb1	Point on object($xRL,-3)[label('b1'), red, layer(10)];
{,label('bSUB{1}'),LabelAlign(5,5),highlight}
$b1	Ratio/Points($OrigoR3,$xykk,$xb1,205,50,'')[red];

$yb2	Point on object($yRL,3)[label('b2'), blue, layer(10)];
{,label('bSUB{2}'),LabelAlign(5,5),highlight}
$b2	Ratio/Points($OrigoR3,$yykk,$yb2,205,65,'')[blue];

$zb3	Point on object($zRL,2)[label('b3'), color(0,150,0), layer(10)];
{,label('bSUB{3}'),LabelAlign(5,5),highlight}
$b3	Ratio/Points($OrigoR3,$zykk,$zb3,205,80,'')[color(0,150,0)];


${
$xb1	Dilation/3PtRatio($xykk,$OrigoR3,$ROb,$Rykkb,$Rptb1)[red,  label('b1')];
$yb2	Dilation/3PtRatio($yykk,$OrigoR3,$ROb,$Rykkb,$Rptb2)[blue, label('b2')];
$zb3	Dilation/3PtRatio($zykk,$OrigoR3,$ROb,$Rykkb,$Rptb3)[color(0,150,0), label('b3')];
$}
$b1b2	VectorTranslation($xb1,$OrigoR3,$yb2)[magenta, label('(b1,b2,0)')];
{,label('( bSUB{1},,bSUB{2},,0)'),LabelAlign(5,5)}
$Sb1b2x	Segment($xb1,$b1b2)[blue];
$Sb1b2y	Segment($yb2,$b1b2)[red];
$SOb1b2	Segment($OrigoR3,$b1b2)[magenta];

$b	VectorTranslation($b1b2,$OrigoR3,$zb3)[black, label('b')];
{,label('\\mathbf{b}'),LabelAlign(5,5)}
$Sbb1b2	Segment($b1b2,$b)[color(0,150,0)];
$Sbb3	Segment($zb3,$b)[black];
$SOb	Segment($OrigoR3,$b)[black,thick];
{,arrowL}

$Rpta11	Point on object($RLa1,4)[label('a11'), red, layer(10),hidden];
{,label('aSUB{11}'), LabelAlign(-5,3), highlight}
$a11	Ratio/Points($ROa1,$Rykka1,$Rpta11,5,50,'')[red];

$Rpta21	Point on object($RLa1,0)[label('a21'), blue, layer(10),hidden];
{,label('aSUB{21}'), LabelAlign(-5,7), highlight}
$a21	Ratio/Points($ROa1,$Rykka1,$Rpta21,5,65,'')[blue];

$Rpta31	Point on object($RLa1,0)[label('a31'),color(0,150,0), layer(10),hidden];
{,label('aSUB{31}'), LabelAlign(-5,10), highlight}
$a31	Ratio/Points($ROa1,$Rykka1,$Rpta31,5,80,'')[color(0,150,0)];

$Rpta12	Point on object($RLa2,0)[label('a12'), red, layer(10),hidden];
{,label('aSUB{12}'), LabelAlign(-5,3), highlight}
$a12	Ratio/Points($ROa2,$Rykka2,$Rpta12,52,50,'')[red];

$Rpta22	Point on object($RLa2,4)[label('a22'),blue, layer(10),hidden];
{,label('aSUB{22}'), LabelAlign(-5,7), highlight}
$a22	Ratio/Points($ROa2,$Rykka2,$Rpta22,52,65,'')[blue];

$Rpta32	Point on object($RLa2,0)[label('a32'),color(0,150,0), layer(10),hidden];
{,label('aSUB{32}'), LabelAlign(-5,10), highlight}
$a32	Ratio/Points($ROa2,$Rykka2,$Rpta32,52,80,'')[color(0,150,0)];


${
the space vectors ALKAA UUSI
$}
$u1	Dilation/3PtRatio($xykk,$OrigoR3,$ROa1,$Rykka1,$Rpta11)[red,  label('a11'),hidden];
$u2	Dilation/3PtRatio($yykk,$OrigoR3,$ROa1,$Rykka1,$Rpta21)[blue, label('a21'),hidden];
$u3	Dilation/3PtRatio($zykk,$OrigoR3,$ROa1,$Rykka1,$Rpta31)[color(0,150,0), label('a31'),hidden];

$u1u2	VectorTranslation($u1,$OrigoR3,$u2)[magenta, label('(a11,a21)'),hidden];
$Su1u2x	Segment($u1,$u1u2)[blue,hidden];
$Su1u2y	Segment($u2,$u1u2)[red,hidden];
$SOu1u2	Segment($OrigoR3,$u1u2)[magenta,hidden];

$U	VectorTranslation($u1u2,$OrigoR3,$u3)[color(255,168,17), label('a1')];
{,label('\\mathbf{a}SUB{1}'), LabelAlign(-5,7)}
$SUu1u2	Segment($u1u2,$U)[color(0,150,0),hidden];
$SOU	Segment($OrigoR3,$U)[color(255,168,17),thick];
{,arrowL}
$SUu3	Segment($u3,$U)[magenta,hidden];

$v1	Dilation/3PtRatio($xykk,$OrigoR3,$ROa2,$Rykka2,$Rpta12)[red,  label('a12'),hidden];
$v2	Dilation/3PtRatio($yykk,$OrigoR3,$ROa2,$Rykka2,$Rpta22)[blue, label('a22'),hidden];
$v3	Dilation/3PtRatio($zykk,$OrigoR3,$ROa2,$Rykka2,$Rpta32)[color(0,150,0), label('a32'),hidden];

$v1v2	VectorTranslation($v1,$OrigoR3,$v2)[magenta, label('(a12,a22)'),hidden];
$Sv1v2x	Segment($v1,$v1v2)[blue,hidden];
$Sv1v2y	Segment($v2,$v1v2)[red,hidden];
$SOv1v2	Segment($OrigoR3,$v1v2)[magenta,hidden];

$V	VectorTranslation($v1v2,$OrigoR3,$v3)[color(255,168,17), label('a2')];
{,label('\\mathbf{a}SUB{2}'), LabelAlign(-5,7)}
$SVv1v2	Segment($v1v2,$V)[color(0,150,0),hidden];
$SOV	Segment($OrigoR3,$V)[color(255,168,17),thick];
{,arrowL}
$SVv3	Segment($v3,$V)[magenta,hidden];

${
The UV-plane
$}
$UplusV	VectorTranslation($U,$OrigoR3,$V)[hidden];
$PlPol	Polygon($OrigoR3,$U,$UplusV,$V)[yellow,layer(14)];
$UminusV	VectorTranslation($U,$V,$OrigoR3)[hidden];
$UminusV	VectorTranslation($U,$V,$OrigoR3)[hidden];
$VminusU	VectorTranslation($V,$U,$OrigoR3)[hidden];
$minusUplusV	VectorTranslation($VminusU,$UplusV,$UminusV)[hidden];
$PUV		Polygon($UplusV,$VminusU,$minusUplusV,$UminusV)[color(236,245,175),layer(5)];


${
The scalar products
$}
$a1x	Calculate(145, 50,'','AB* CD* +')($a11,$x1,$a12,$x2)[red,hidden];
$a2x	Calculate(145, 65,'','AB* CD* +')($a21,$x1,$a22,$x2)[blue,hidden];
$a3x	Calculate(145, 80,'','AB* CD* +')($a31,$x1,$a32,$x2)[color(0,150,0),hidden];

$RptAx1 Dilation/MarkedRatio($xykk,$OrigoR3,$a1x)[red,label('b1'''),hidden];
$RptAx2 Dilation/MarkedRatio($yykk,$OrigoR3,$a2x)[blue,label('b2'''),hidden];
$RptAx3 Dilation/MarkedRatio($zykk,$OrigoR3,$a3x)[color(0,150,0),label('b3'''),hidden];

$SOR3RptAx1 Segment($RptAx1,$OrigoR3)[red,hidden];
$SOR3RptAx2 Segment($RptAx2,$OrigoR3)[blue,hidden];

$b1b2pr	VectorTranslation($RptAx1,$OrigoR3,$RptAx2)[magenta, label('(b1'',b2'')'),hidden];
{,label('( bSUB{1}'',bSUB{2}'',0)'),LabelAlign(5,5)}
$Sb1b2pr1 Segment($RptAx1,$b1b2pr)[blue,hidden];
{,dash(1)}
$Sb1b2pr2 Segment($RptAx2,$b1b2pr)[red,hidden];
{,dash(1)}
$SOb1b2pr	Segment($OrigoR3,$b1b2pr)[magenta,hidden];

$bpr	VectorTranslation($b1b2pr,$OrigoR3,$RptAx3)[color(120,60,0), label('b'''),hidden];
{,label('\\mathbf{b}'''),LabelAlign(5,10)}
$Sbb1b2pr	Segment($b1b2pr,$bpr)[color(0,150,0),hidden];
{,dash(1)}
$SObpr		Segment($OrigoR3,$bpr)[color(120,60,0),thick,hidden];
{,arrowL}
$xa1 	Dilation/MarkedRatio($U,$OrigoR3,$x1)[color(120,60,0),hidden];
$SOxa1 	Segment($OrigoR3,$xa1)[color(120,60,0),layer(30),hidden];
$Sxa1bpr Segment($xa1,$bpr)[color(120,60,0),hidden];
$xa2 	Dilation/MarkedRatio($V,$OrigoR3,$x2)[color(120,60,0),hidden];
$SOxa2 	Segment($OrigoR3,$xa2)[color(120,60,0),layer(30),hidden];
$Sxa2bpr Segment($xa2,$bpr)[color(120,60,0),hidden];


{ The least squares solution X }
$A	Calculate(205, 10,'A = ','A2^ B2^ + C2^ +')($a11,$a21,$a31)[black,hidden];	
$B	Calculate(205, 25,'B = ','AD* BE* + CF* +')($a11,$a21,$a31,$a12,$a22,$a32)[black,hidden];
$C	Calculate(205, 40,'C = ','A2^ B2^ + C2^ +')($a12,$a22,$a32)[black,hidden];	
$D	Calculate(205, 55,'D = ','AD* BE* + CF* +')($a11,$a21,$a31,$b1,$b2,$b3)[black,hidden];
$E	Calculate(205, 70,'E = ','AD* BE* + CF* +')($a12,$a22,$a32,$b1,$b2,$b3)[black,hidden];
$det	Calculate(205, 85,'det = ','AC* BB* -')($A,$B,$C)[black,hidden];
$X1	Calculate(140,120,'','AD* BC* - E /')($D,$B,$E,$C,$det)[black, hidden];
$X1text FixedText(195,120, '')[black, hidden];
{,text('\\( \\hat xSUB{1} \\ = \\)' )}
$X2	Calculate(140,140,'','AD* BC* - E /')($A,$D,$B,$E,$det)[black, hidden];
$X2text FixedText(195,140, '')[black hidden];
{,text('\\( \\hat xSUB{2} \\ = \\)' )}
$RptX1	Dilation/MarkedRatio($xykkR2,$OrigoR2,$X1)[black, label('X1'),hidden];
{,label('\\hat xSUB{1}')}
$RptX2  Dilation/MarkedRatio($yykkR2,$OrigoR2,$X2)[black,label('X2'),hidden];
{,label('\\hat xSUB{2}')}

$X	VectorTranslation($RptX1,$OrigoR2,$RptX2)[magenta, label('X'),hidden];
{,label('\\hat{ \\mathbf{x}}')}
$Xtr	VectorTranslation($RptX1,$OrigoR2,$RptX2)[magenta, label('X'),hidden,traced];
{,label('\\hat{ \\mathbf{x}}')}
$SXX1	Segment($RptX1,$X)[blue,hidden];
$SXX2	Segment($RptX2,$X)[red,hidden];
$SOX	Segment($OrigoR2,$X)[magenta,hidden];

$ALeUp	FixedPoint(0,42)[hidden];
$ARiUp	FixedPoint(90,42)[hidden];
$ARiLo	FixedPoint(90,90)[hidden];
$ALeLo	FixedPoint(  0,90)[hidden];
$APol	Polygon($ALeUp,$ARiUp,$ARiLo,$ALeLo)[yellow];

$xLeUp	FixedPoint(103,45)[hidden];
$xRiUp	FixedPoint(125,45)[hidden];
$xRiLo	FixedPoint(125,78)[hidden];
$xLeLo	FixedPoint(103,78)[hidden];
$xPol	Polygon($xLeUp,$xRiUp,$xRiLo,$xLeLo)[color(220,220,220)];

$xLeUp2	FixedPoint( 0,110)[hidden];
$xRiUp2	FixedPoint(87,110)[hidden];
$xRiLo2	FixedPoint(87,150)[hidden];
$xLeLo2	FixedPoint( 0,150)[hidden];
$xPol2	Polygon($xLeUp2,$xRiUp2,$xRiLo2,$xLeLo2)[color(220,220,220)];

$bprLeUp	FixedPoint(140,42)[hidden];
$bprRiUp	FixedPoint(190,42)[hidden];
$bprRiLo	FixedPoint(190,90)[hidden];
$bprLeLo	FixedPoint(140,90)[hidden];
$bprPol	Polygon($bprLeUp,$bprRiUp,$bprRiLo,$bprLeLo)[color(240,200,200),hidden];

$bLeUp	FixedPoint(202,42)[hidden];
$bRiUp	FixedPoint(245,42)[hidden];
$bRiLo	FixedPoint(245,90)[hidden];
$bLeLo	FixedPoint(202,90)[hidden];
$bPol	Polygon($bLeUp,$bRiUp,$bRiLo,$bLeLo)[color(200,240,200)];

$ObPolprPlane	Polygon($OrigoR3,$xa1,$bpr,$xa2,$OrigoR3)[color(200,150,100),layer(15),hidden];
$ObPol		Polygon($OrigoR3,$b,  $b1b2,  $OrigoR3)[color(200,240,200),layer(20)];
$ObPolpr	Polygon($OrigoR3,$bpr,$b1b2pr,$OrigoR3)[color(240,200,200),layer(19),hidden];

$SBXtr	ShowButton( 0,160,'Trace X')($Xtr)[blue,hidden];
{,text('Trace \\( \\hat{ \\mathbf{x}}\\)')}
$HBXtr	HideButton(60,160,'Stop')($Xtr)[blue,hidden];	

$SBX	ShowButton(100,83,'LSQR X')($X1,$X2,$RptX1,$RptX2,$X1text,$X2text,$X,$SXX1,$SXX2,$SOX,$SBXtr,$HBXtr)[magenta,bold];
{,text('LSQR \\( \\hat{ \\mathbf{x}}\\)')}
$HBX	HideButton(163,83,'Hide')(  $X1,$X2,$RptX1,$RptX2,$X1text,$X2text,$X,$SXX1,$SXX2,$SOX,$SBXtr,$HBXtr)[magenta];


$SBRL	ShowButton(  0,345,'Change A')($ROa1,$ROa2,$R1a1,$R1a2,$SRLa1,$SRLa2,$Rpta11,$Rpta12,$Rpta21,$Rpta22,$Rpta31,$Rpta32,$RectA)[black,bold];
{,text('Change \\(  A\\)')}
$HBRL	HideButton(70,345,'Fix')(      $ROa1,$ROa2,$R1a1,$R1a2,$SRLa1,$SRLa2,$Rpta11,$Rpta12,$Rpta21,$Rpta22,$Rpta31,$Rpta32,$RectA)[black];

$SRes	Segment($b,$bpr)[blue,thick,hidden];
$Res	Calculate(350, 80,'','AB- 2^ CD- 2^ + EF- 2^ + @sqrt')($b1,$a1x,$b2,$a2x,$b3,$a3x)[blue,hidden];
$ResText FixedText(480,80, '')[blue, hidden];
{,text('\\( \\left| \\, A \\mathbf{x} - \\mathbf{b} \\, \\right| \\ =  \\)')}

$SBRes	ShowButton(260,40,'Residual')($Res,$SRes,$ResText,$AxText,$a1x,$a2x,$a3x,$eqsign,$bprPol,$bpr,$SObpr)[blue,bold];
$HBRes	HideButton(320,40,'Hide')(    $Res,$SRes,$ResText)[blue];

$SBAx	ShowButton(125,0,'b'' = Ax')($AxText,$a1x,$a2x,$a3x,$eqsign,$bprPol,$bpr,$SObpr)[color(230,140,140),bold];
{,text('\\( \\mathbf{b}'' = A \\mathbf{x}\\)')}
$HBAx	HideButton(190,0,'Hide')(    $AxText,$a1x,$a2x,$a3x,$eqsign,$bprPol,$bpr,$SObpr,$b1b2pr,$Sb1b2pr1,$Sb1b2pr2,$SOb1b2pr,$Sbb1b2pr,$ObPolpr,$xa1,$SOxa1,$Sxa1bpr,$xa2,$SOxa2,$bpr,$SObpr,$Sxa2bpr,$SRes,$Res)[color(230,140,140)];

$SBAxInSpace	ShowButton(240,0,'b'' = Ax in space')($AxText,$a1x,$a2x,$a3x,$eqsign,$bprPol,$b1b2pr,$Sb1b2pr1,$Sb1b2pr2,$SOb1b2pr,$bpr,$SObpr,$Sbb1b2pr,$ObPolpr,$SOR3RptAx1,$SOR3RptAx2)[color(230,140,140),bold];
{,text('\\( \\mathbf{b}'' = A \\mathbf{x}\\) in space')}
$HBAxInSpace	HideButton(350,0,'Hide')(             $b1b2pr,$Sb1b2pr1,$Sb1b2pr2,$SOb1b2pr,$Sbb1b2pr,$ObPolpr,$SOR3RptAx1,$SOR3RptAx2)[color(230,140,140)];

$SBAxInPlane ShowButton(390,0,'b'' = Ax in plane')($xa1,$SOxa1,$Sxa1bpr,$xa2,$SOxa2,$bpr,$SObpr,$Sxa2bpr,$ObPolprPlane)[color(120,60,0),bold];
{,text('\\( \\mathbf{b}'' = A \\mathbf{x}\\) in plane')}
$HBAxInPlane HideButton(500,0,'Hide')(             $xa1,$SOxa1,$Sxa1bpr,$xa2,$SOxa2,$Sxa2bpr,$ObPolprPlane)[color(120,60,0)];


$SBeq	ShowButton( 5,0,'Equation')($a11,$a12,$b1,$a21,$a22,$b2,$a31,$a32,$b3,$AText,$xText,$x1Text,$x2Text,$eqsign,$bText,$APol,$xPol,$bPol)[black,bold];
$HBeq	HideButton(65,0,'Hide')(   $a11,$a12,$b1,$a21,$a22,$b2,$a31,$a32,$b3,$AText,$xText,$x1Text,$x2Text,$eqsign,$bText,$APol,$xPol,$bPol)[black,bold];
</JSP>