Question

Matrix M has x-rows and (11-x) columns. Matrix N has y-rows and (y+5) columns. If MN and NM both are defined, find the values of x and y​

Answer 1

`x=8, y=3`

Explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

`y=11-x----(1)`

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

`y+5=x----(2)`

Substitute (1) into (2):

`11-x+5=x\\2x=16\\\therefore x=8--(3)`

Substitute (3) into (1):

`y=11-8=3`