Matrix multiplication from the right with inverse matrix

a=[-0.7398 1.638; 1.4522 -4.258; 2.192 5.42];
r=[2.74 1.6; 0 6.9; 0 0];
u=a\r;
u

I know it's a trivia question but I'm just a begginer and it's really bugging me out.

I have this equation: U=R*A^-1 . From the documentation I found out that u=a/r calculates U=A^-1*R. I've been spilling my brains out trying to find a way to get this equation right but some of the possible answers I found only made me more confused.

Can someone please show me a possible way to implement this equation U=R*A^-1 in matlab and to work properly?

Answer 1

[Ameer Hamza]

You can use mrdivide /

u = r/a

The equation is equivalent to . mrdivide is used for such equations.

[George Rosca]

u=r/a returns a 3x3 matrix

u=a\r (U=A^-1*R) returns a 2x2 matrix, and even though it's not correct because I need the multiplication from the right, I believe it's closer to reality in terms of size.

Edit: u=r/a returns a 3x3 matrix but with the first column and the last line full of zeros, I tend to believe that it might be correct but I need to delete the respective column and line, could this be true?

[John D'Errico]

No. If you delete the zero column and the zero row, then you CANNOT form the product of a 2x2 matrix times a 3x2 matrix in that order. This is basic linear algebra, how you multiply matrices.

Answer 2

[John D'Errico]

a is a 3x2 matrix. No matter what, you cannot compute the inverse of a, so

U=R*A^-1

is meaningless.

I assume you want to solve for the matrix U, such that

U*a == r

as closely as possible. That is, norm(U*a-r) is the smallest possible value over all matrices U?

a=[-0.7398 1.638; 1.4522 -4.258; 2.192 5.42];
r=[2.74 1.6; 0 6.9; 0 0];

In the help for / (known as mrdivide if you look at the function itself) we see:

>> help /

/ Slash or right matrix divide.

A/B is the matrix division of B into A, which is roughly the

same as A*INV(B) , except it is computed in a different way.

So, if you could invert the matrix you call a, we would perform your task as:

 U = r/a;

Does u have the desired property? Yes.

 norm(U*a- r)

ans = 9.9301e-16

As we see, the norm is effectively zero, or as close as we could come in floating point arithmetic.

 r

r = 3×2

2.7400 1.6000 0 6.9000 0 0

 U*a

ans = 3×2

2.7400 1.6000 -0.0000 6.9000 0 0

The matrix U is a 3x3 matrix. as in order for the sizes of the matrices to conform for matrix multiplication, it must have that size.

 U

U = 3×3

0 0.6593 0.8132 0 -0.8791 0.5824 0 0 0

●

As you can see, U is 3x3. Remember how you multiply matrices. If you wish to form the product U*a, where a is 3x2, and have the result be a matrix of size 3x2 also, then U MUST be a 3x3 matrix.