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1;
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> restart; with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected
"
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! !5 "
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#$ %
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vector() *
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5
%" $ ;
> restart: with(linalg):
u:=vector([1,2,3,4]);
" $"
$!
!
Warning, the protected names norm and trace have been redefined and
unprotected
;< = 0( 6( 7( 8 >
"
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vector() ! 5
> v:=vector(5);
%
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8
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*
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> evalm(v);
?
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?
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%
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> w1:=[1,2,3,4,5,6];
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;< = 0( 6( 7( 8( ?( @ >
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! " "$"
$ 2 % ! " "! $
> w2:=matrix(1,3,[a,b,c]);
w3:=matrix(3,1,[d,e,f]);
;< =
>
;<
+
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!
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> B1:=basis({vector([1,1,1]),vector([1,1,0]),vector([2,2,1]),ve
ctor([1,0,0])});
;< A = 0( 0( 0 >( = 0( 0( C >( = 0( C(C > B
> B2:=basis([vector([1,1,1]),vector([1,1,0]),vector([2,2,1]),ve
ctor([1,0,0])]);
! "$
;< = = 0( 0( 0 >( = 0( 0( C >( = 0( C( C > >
" dotproduct(v,w) "#
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%
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3"
> F(a*u);
=
0
+
6
+
7(
−
0
−
7>
> a*F(u);
= 0+ 6 + 7( − 0 − 7 >
'%
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'!
!%
!!" 3" ! 2 ! "$ "
4;
> simplify(evalm(F(a*u)-a*F(u)));
!" $ $" *
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= C( C >
;
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! "$ "
3 */4*3./#0,4*3./ 0,$$$,4*3./ 00,/3/#0,3/ 0,$$$,3/ 00. "
$
$2
;
> A:= genmatrix([F(x)[1],F(x)[2]],[x[1],x[2],x[3]]);
;<
" $" '
%
("
- $ !"( *
! $5
00 0
J0 C J0
! $'
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7
! ' " =0(J0> & * ! $ 5
!)! $" ' "
!#
$ $" ' !" ( *
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!
$ & )! $ "! $
> F([1,0,0]);F([0,0,1]);
1
!$
!
!#
1
7
$# /
";
2
!
= 0( J0 >
= 0( J0 >
( " $"
'%
* !$ 2
!"
! 2 ! "$ "
%
&
;
> x:=vector(3):equal(F(x),A&*x); evalm(F(x)-A&*x);
!5
%
1!
!
3 ! "$ "4
"
" "$ "4,
! "$ " 6
* . 3"
! )!" ! %
1!
> kernel(A);
!
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= C( C >
" ' " ! %" $ " " " " !" '...
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