Chapter 4.3, Problem 40PPS

To determine

To find:The result of given operation

Answer to Problem 40PPS

The result of givenoperation is $\left[\begin{array}{c}30+36.75x+50.25x\\ -6x^2-13.5y^2-18x-12y-10.5xy-12\\ -78-83.4x-94.2y\end{array}\right]$

Explanation of Solution

Given information:

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

Calculation:

The value of is, $\left(YX\right)Z$

  $\begin{array}{c}\left(YX\right)Z=\left(\left[\begin{array}{cc}-5& -1.5\\ x+2& y\\ 13& 1.2\end{array}\right]\left[\begin{array}{cc}2& -6\\ 3y& -4.5\end{array}\right]\right)\left[\begin{array}{c}-3\\ x+y\end{array}\right]\\ =\left[\begin{array}{cc}-10-4.5y& 36.75\\ 2x+4+3y^2& -6x-4.5y-12\\ 3.6y+26& -83.4\end{array}\right]\left[\begin{array}{c}-3\\ x+y\end{array}\right]\\ =\left[\begin{array}{c}30+36.75x+50.25x\\ -6x^2-13.5y^2-18x-12y-10.5xy-12\\ -78-83.4x-94.2y\end{array}\right]\end{array}$

Thus, the result of the operation is $\left[\begin{array}{c}30+36.75x+50.25x\\ -6x^2-13.5y^2-18x-12y-10.5xy-12\\ -78-83.4x-94.2y\end{array}\right]$