(b) What is one solution to the system Ax = c? . The purpose of this problem is

Question

(b) What is one solution to the system Ax = c? . The purpose of this problem is to show that scalar matrices commute with any other matrix. Let A- (ay] be a scalar matrix and let B - by] be any square matrix of the same size. In addition, let Let AB = [cil and BA = [dij] (a) What can you conclude about the entries of A because it is assumed to be a scalar (b) Use the definition of matrix multiplication and part (a) to compute ciy in terms (c) Use the definition of matrix multiplication and part (a) to compute dj in terms (d) What is the definition of equal matrices, and what can you now conclude about matrix? of the entries of A and B of the entries of A and B AB and BA?

Explanation / Answer

a) matrix A is a scalar matrix so the entries in its diagnol are the same.

^A
b)Since B is a square matrix so it can be :-

So AB =  

c) BA =

d) Equal matrices are those in which the number of rows of the matrices are equal and number of colmuns of both the matrices are equal and the corresponding entries in each matrix are equal.
So, by this definition, AB and BA are eqaul matrices.

1 0 0 0 1 0 0 0 1

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