1. ## 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.

2. 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 $I_{rs}$ is a binary matrix (all its elements are either $0$ or $1$) but more than that, I can't say.

All I can say for sure so far, is that, if $I_{rs}A$ is meaningful, then the number of columns in $I_{rs}$ is the same as the number of rows in $A$. So $I_{rs}$ is a $l\times m$ matrix, for some value of $l$, and the order of the resulting product will be $l \times n$.

Can anyone else shed any light on this?

Let $A = (a_{ij})$ be an m x n matrix. Let r and s be between or equal to 1 to m. Let $I_{rs}$ be the m×m matrix whose (r,s)-component is 1 and such that all other components are equal to 0.
(a) What is $I_{rs}A$?
First, as Grandad says, the number of columns of $I_{rs}$ must be the same as the number of rows of A (otherwise the product $I_{rs}A$ is not defined). Second, I'm guessing that $I_{rs}$ is meant to be a square matrix, so that the product $I_{rs}A$ will have the same number of rows and columns as A.
If the only nonzero component of $I_{rs}$ is a 1 in row r and column s, then you should be able to see that the only nonzero components of $I_{rs}A$ will be in row r. What's more, the element in the (r,j)-position in $I_{rs}A$ will be the (s,j)-component of A. So row r of $I_{rs}A$ will be the same as row s of A, and all the other rows of $I_{rs}A$ will consist of zeros.