Chapter 8, Problem 38RE

To determine

Find thevalue of $x$ and $y$ using the equality of matrices.

Answer to Problem 38RE

The value of $x=8\text{and}y=0$ .

Explanation of Solution

Given information:

The givenmatrix equation is

  $\left[\begin{array}{cc}-1& 0\\ x& 5\\ -4& y\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 8& 5\\ -4& 0\end{array}\right]$

Calculation:

Two matrices $A=\left[a_{ij}\right]$ and $B=\left[b_{ij}\right]$ are equal when they have the same order $m\times n$ and $a_{ij}=b_{ij}$ for

  $1\le i\le m$ and $1\le j\le n$ . In other words, two matrices are equal when their corresponding entries are equal.

The given matrix equation is $\left[\begin{array}{cc}-1& 0\\ x& 5\\ -4& y\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 8& 5\\ -4& 0\end{array}\right]$ and both matrices are equal.

Two matrices are equal when their corresponding entries are equal.

Hence thevalue of $x=8\text{and}y=0$ .