2*[3 4]
[2*3 2*4]
A=rand(1:3,2,4); B=rand(1:3,4,3); C=rand(1:3,4,2);
println( A*[B C])
println( [A*B A*C])
rand3(n)=rand(1:3,n,n); # define rand3 (A little shorthand)
I=eye(3); A=rand3(3); M=inv(A); # Might be singular, careful (single exception or large numbers indicate singularity)
I=eye(3);
showcompact(
M*[A I] ); println('\n')
showcompact(
[ I M]
)
Z=[ A I]
Z[2,:] -= (Z[2,1]/Z[1,1])*Z[1,:];Z # Method 1. (Easier for Programming) Elimination via row operations
Z=[ A I];
E=copy(I); E[2,1]=-Z[2,1]/Z[1,1];E # Method 2: Create an elimination matrix with the negative multiplier in the (2,1) position, say
Z=E*Z
Z[3,:] -= (Z[3,1]/Z[1,1])*Z[1,:];Z
Z[1,:] -= (Z[1,2]/Z[2,2])*Z[2,:];Z
Z[3,:] -= (Z[3,2]/Z[2,2])*Z[2,:];Z
Z[1,:] -= (Z[1,3]/Z[3,3])*Z[3,:];Z
Z[2,:] -= (Z[2,3]/Z[3,3])*Z[3,:];Z
Z[1,:]/=Z[1,1];Z
Z[2,:]/=Z[2,2];Z
Z[3,:]/=Z[3,3];Z
inv(A)
A=[ 6.0 5 10; 8 13 8; 3 14 7]; Aoriginal=copy(A);
A[2,:]-= (4/3)*A[1,:]
A
A[3,:] -= ( 0.5 )*A[1,:]
A
A[3,:]-= (11.5/6.333333 )*A[2,:];A
U=ans
(11.5/6.333333 )
69/38
U
L=eye(3)
L[2,1]=4/3; L[3,1]=0.5; L[3,2]=69/38;L
L*U
Aoriginal
E
inv(E)
M=rand(3,3)
E*M
inv(E)* (E*M)