Chapter 3.6, Problem 38PPS

To determine

To find: Matrix $ZY$ if defined

Explanation of Solution

Given information: $X=\left[\begin{array}{cc}2& -6\\ 3y& -4.5\end{array}\right],Y=\left[\begin{array}{cc}-5& -1.5\\ x+2& y\\ 13& 1.2\end{array}\right],Z=\left[\begin{array}{c}-3\\ x+y\end{array}\right]$

Formula used: Product of matrices A and B that is AB is possible if number of columns in matrix A is equal to number of rows in matrix B

Proof:

Consider the matrix $Z=\left[\begin{array}{c}-3\\ x+y\end{array}\right]$

Here, number of columns = 1

Now consider the matrix $Y=\left[\begin{array}{cc}-5& -1.5\\ x+2& y\\ 13& 1.2\end{array}\right]$

Here, number of rows = 3

As number of columns in matrix Z is not equal to number of rows in matrix Y,

  $ZY$ Is undefined.