Thread: Matrix Multiplication

Let A = (aij) be an m x n matrix. Let r and s be between or equal to 1 to m. Let Irs be the matrix whose rs-composition is 1 and such that all other components are equal to 0.

(a) What is IrsA.

I'm totally confused, can someone explain where to begin.

Hello millerst

Originally Posted by millerst

Let A = (aij) be an m x n matrix. Let r and s be between or equal to 1 to m. Let Irs be the matrix whose rs-composition is 1 and such that all other components are equal to 0.

(a) What is IrsA.

I'm totally confused, can someone explain where to begin.

I don't know what this bit means.

...Let Irs be the matrix whose rs-composition is 1...

Have you been given an explanation of this? It sounds as if is a binary matrix (all its elements are either or ) but more than that, I can't say.

All I can say for sure so far, is that, if is meaningful, then the number of columns in is the same as the number of rows in . So is a matrix, for some value of , and the order of the resulting product will be .

Can anyone else shed any light on this?

Grandad

Here's my interpretation of the question.

Originally Posted by millerst

Let be an m x n matrix. Let r and s be between or equal to 1 to m. Let be the m×m matrix whose (r,s)-component is 1 and such that all other components are equal to 0.

(a) What is ?

First, as Grandad says, the number of columns of must be the same as the number of rows of A (otherwise the product is not defined). Second, I'm guessing that is meant to be a square matrix, so that the product will have the same number of rows and columns as A.

If the only nonzero component of is a 1 in row r and column s, then you should be able to see that the only nonzero components of will be in row r. What's more, the element in the (r,j)-position in will be the (s,j)-component of A. So row r of will be the same as row s of A, and all the other rows of will consist of zeros.