Question

show that if A is a m*n matrix and A*(B*A) exists then B ia a n*m matrix

Answer 1

In general terms you an calculate the product of two matrices X and Y if X is m x n and Y is n x p. The resulting matrix XY is m x p

Hence if BA exists then as A is m x n, it must be that B is j x m for some j.

The resulting matrix BA is j x n.
We now multiply that matrix by the m x n matrix A, then j must be equal to n.

Therefore B is a j x m = n x m matrix.

Answer 2

thank you

Answer 3

Schematically, we can see it one go, like this. Let B have dimensions j x k

Then the product ABA is a product of matrices

m x n . j x k . m x n

So it must be that j = n and k = m.

Hence B is n x m.

Answer 4

i have this one show that the sum of the elements of principal diagonal of (A+B)=sum of the elements of principal diagonal A+sum of the elements of principal diagonal B.....A and B are matrix thank you in advance

Answer 5

ok

Answer 6

i'm new so i don't know what to do and i'm so stressed out with these