If 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 and 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finda) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYnUSJBRidGMkY1RjhGOy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZC, the vector projection of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn along LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiQUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn, and
b) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21vR0YkNi1RJyZwZXJwO0YnL0Y5USdub3JtYWxGJy8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtRi82J1EiQUYnRjJGNUY4RjtGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkM=, the component of B orthogonal to A.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn
<Text-field style="Heading 1" layout="Heading 1">Solution by Task Template</Text-field>JSFH
Enter vectors A and BUsing the Matrix palette, create the column vector A.Context Menu: Assign to a Name\342\211\273AJSFHUsing the Matrix palette, create the column vector B.Context Menu: Assign to a Name\342\211\273BJSFHTools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Projection Plot: onto 1D
Projection onto 1-D SubspaceVector to be projectedProject onto
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%RadioButton7)=false then
Do(%ComboBox3(enabled)=false);
Do(%Label6(enabled)=false);
Do(%Label7(enabled)=false);
end if;
end use;
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%RadioButton6)=false then
Do(%ComboBox3(enabled)=true);
Do(%Label6(enabled)=true);
Do(%Label7(enabled)=true);
end if;
end use;
[x\134,y],otheruse DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
if Do(%ComboBox3)=[x,y] then Do(%MathContainer21=NULL);end if;
end use;
use DocumentTools,plots, Student[LinearAlgebra] in
module()
local B,A,X,Y,Z,q1,q2,FIG, temp;
Do(B = %MathContainer18):
if Do(%RadioButton6) then Do(A = %MathContainer19);
if nops([A])=0 then Do(%Plot3 = display(textplot([0,0,"Provide a vector onto which to project"]),axes=none));
else
if Dimension(A)<>Dimension(B) then Do(%Plot3 = display(textplot([0,0,"Vectors should have the same dimension"]),axes=none));return;
elif nops(select(type,indets(A),name))<>0 or nops(select(type,indets(B),name))<>0 then Do(%Plot3 = display(textplot([0,0,"No graph can be drawn if vectors are not numeric"]),axes=none));return;
elif Dimension(A)=2 and Dimension(B)=2 then
FIG := ProjectionPlot(B,A, title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black]):
elif Dimension(A)=3 and Dimension(B)=3 then
FIG := ProjectionPlot(B,A, title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black], axes=box,labels=[x,y,z],orientation=[-55,50]):
end if;
Do(%Plot3 = FIG):
end if;
end if;
if Do(%RadioButton7) then
if Dimension(B)=3 and Do(%ComboBox3)=[x,y] then Do(%Plot3 = display(textplot([0,0,"Variables can't be [x,y] in 3D"]),axes=none));return;end;
if Dimension(B)=3 and Do(%ComboBox3)=other then Do(temp = %MathContainer21);
if nops([temp])=0 then Do(%MathContainer21 = MathML[Export]("???"));return;end if;
X:=temp[1];Y:=temp[2];Z:=temp[3];
Do(A = %MathContainer20);
FIG := ProjectionPlot(B,A, [X,Y,Z],title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black], axes=box,labels=[X,Y,Z],orientation=[-55,50]):
Do(%Plot3 = FIG);
return;end if;
if Do(%ComboBox3)=[x,y] then X:=x;Y:=y;end if;
if Do(%ComboBox3)=other then Do(temp=%MathContainer21);X:=temp[1];Y:=temp[2];end if;
Do(q1 = %MathContainer20);
if is(q1=NULL) then
Do(%MathContainer23=MathML[Export]("Provide equation of a line thru origin"));
else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if;
if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer22=MathML[Export]("Declared variables must match those in equation of line"));return;end if;
if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer23=MathML[Export]("The line does not pass thru origin"));
else
FIG := ProjectionPlot(B,q2,[X,Y], title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black]);
Do(%Plot3 = FIG);
end if;
end if;
end if;
end module;
end use;
use DocumentTools in
# Enter Maple commands to be executed when the specified
# action is carried out on the component.
# Use:
# Do( %component_name );
# and
# Do( %component_name = value );
# to set and get properties of the component.
# You can also use arbitrary expressions
# involving components, e.g.:
# Do( %target = %input1 + 2*%input2 );
# Note the %-prefix to each component name.
# See ?CustomizingComponents for more information.
Do(%MathContainer18 = NULL);
Do(%MathContainer23 = NULL);
Do(%MathContainer19 = NULL);
Do(%MathContainer20 = NULL);
Do(%MathContainer22 = NULL);
Do(%MathContainer21 = NULL);
Do(%Plot3 = plots[display](plots[textplot]([0,0," "]),axes=none));
end use;
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use DocumentTools, Student[LinearAlgebra] in
module()
local B,A,BA,q1,q2,X,Y,temp,Temp;
Do(B = %MathContainer18):
if Do(%RadioButton6) then Do(A = %MathContainer19);
if nops([A])=0 then Do(%MathContainer22 = MathML[Export]("Provide a vector onto which to project"));
else
Temp := GetProperty(MathContainer23,value);
if StringTools:-Has(Temp,"P") then Do(%MathContainer23 = NULL);end if;
if Dimension(B)=Dimension(A) then
BA:=(B.A)/(A.A)*A;
Do(%MathContainer22 = BA);
else Do(%MathContainer22 = MathML[Export]("Vectors should have the same dimension"));return;end if;
end if;
end if;
if Do(%RadioButton7) then
if Dimension(B)=3 and Do(%ComboBox3)=[x,y] then Do(%MathContainer22 = MathML[Export]("Variables can't be [x,y] in 3D"));return;end if;
if Dimension(B)=3 and Do(%ComboBox3)=other then
Do(A = %MathContainer20);
BA := (B.A)/(A.A)*A;
Do(%MathContainer22 = BA);
return;
end if;
if Do(%ComboBox3)=[x,y] then X:=x;Y:=y;end if;
if Do(%ComboBox3)=other then Do(temp=%MathContainer21);X:=temp[1];Y:=temp[2];end if;
Do(q1 = %MathContainer20);
if is(q1=NULL) then
Do(%MathContainer22=MathML[Export]("Provide equation of a line thru origin"));
else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if;
if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer22=MathML[Export]("Declared coordinates must match variables in equation of line"));return;end if;
if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer22=MathML[Export]("The line does not pass thru origin"));
else
if has(q2,X) and has(q2,Y) then A:=<1,coeff(solve(q2,Y),X)>;BA:=(B.A)/(A.A)*A;Do(%MathContainer22 = BA);
elif has(q2,X) and not has(q2,Y) then BA:=<0,B[2]>;Do(%MathContainer22 = BA);
else BA:=<B[1],0>;Do(%MathContainer22 = BA); end if;
end if;
end if;
end if;
end module;
end use;
use DocumentTools in
module()
local temp;
try
GetProperty(MathContainer22,expression);
catch:
return;
end try;
Do(temp = %MathContainer22);
if nops([temp])=0 then return;end if;
Do(%MathContainer22 = evalf(temp));
end module;
end use;
use DocumentTools, Student[LinearAlgebra] in
module()
local A,B,BA,BpA,q1,q2,X,Y,temp;
Do(B = %MathContainer18):
if Do(%RadioButton6) then Do(A = %MathContainer19);
if nops([A])=0 then Do(%MathContainer23 = MathML[Export]("Provide a vector onto which to project"));
else
temp := GetProperty(MathContainer22,value);
if StringTools:-Has(temp,"P") then Do(%MathContainer22 = NULL);end if;
if Dimension(B)=Dimension(A) then
BA:=(B.A)/(A.A)*A;
BpA:=B-BA;
Do(%MathContainer23 = BpA);
else Do(%MathContainer23 = MathML[Export]("Vectors should have same dimension"));return;end if;
end if;
end if;
if Do(%RadioButton7) then
if Dimension(B)=3 and Do(%ComboBox3)=[x,y] then Do(%MathContainer23 = MathML[Export]("Variables can't be [x,y] in 3D"));return;end if;
if Dimension(B)=3 and Do(%ComboBox3)=other then
Do(A = %MathContainer20);
BA := (B.A)/(A.A)*A;
BpA := B-BA;
Do(%MathContainer23 = BpA);
return;
end if;
if Do(%ComboBox3)=[x,y] then X:=x;Y:=y;end if;
if Do(%ComboBox3)=other then Do(temp=%MathContainer21);X:=temp[1];Y:=temp[2];end if;
Do(q1 = %MathContainer20);
if is(q1=NULL) then
Do(%MathContainer23=MathML[Export]("Provide equation of a line thru origin"));
else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if;
if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer23=MathML[Export]("Declared coordinates must match variables in equation of line"));return;end if;
if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer23=MathML[Export]("The line does not pass thru origin"));
else
if has(q2,X) and has(q2,Y) then A:=<1,coeff(solve(q2,Y),X)>;BA:=(B.A)/(A.A)*A;BpA:=B-BA;Do(%MathContainer23 = BpA);
elif has(q2,X) and not has(q2,Y) then BpA:=<B[1],0>;Do(%MathContainer23 = BpA);
else BpA:=<0,B[2]>;Do(%MathContainer23 = BpA); end if;
end if;
end if;
end if;
end module;
end use;
use DocumentTools in
module()
local temp;
try
GetProperty(MathContainer23,expression);
catch:
return;
end try;
Do(temp = %MathContainer23);
if nops([temp])=0 then return;end if;
Do(%MathContainer23 = evalf(temp));
end module;
end use;
with(Student:-LinearAlgebra):JSFH
<Text-field style="Heading 1" layout="Heading 1">Interactive Solution (from First Principles)</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Implement the formula 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
(The dot is found on both the Common Symbols and Operators palettes.)Press the Enter key.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnTo obtain LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21vR0YkNi1RJyZwZXJwO0YnL0Y5USdub3JtYWxGJy8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtRi82J1EiQUYnRjJGNUY4RjtGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkM=, compute 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, referencing LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2Ji1GLzYnUSJBRidGMkY1RjhGO0YyRjhGOy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y5USdub3JtYWxGJw== by its equation label.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn