Chapter 16, Problem 1CT

To determine

To find: The value of $x$ and $y$ .

Answer to Problem 1CT

The value of $x$ is $3$ , and $y$ is $-4.$

Explanation of Solution

Given information:

The given expression

  $o_{1\times 3}=\left[\begin{array}{c}2x-6\\ 0\\ y+4\end{array}\right]$

Calculation:

Consider the expression

We know that $o_{3\times 1}$ is a $3\times 1$ matrix in which each element is zero. It has $3$ rows and 1

Column.

  $o_{3\times 1}=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]$

Thus,

  $\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}2x-6\\ 0\\ y+4\end{array}\right]$

If two matrices have the same dimensions and the elements in all corresponding positions are equal, then the matrices are equal.

Since the matrices are equal, equate the elements in corresponding positions.

  $\begin{array}{r}2x-6=0\\ y+4=0\end{array}$

Solve for $x$ .

Add $6$ to each side of $2x-6=0$ .

  $\begin{array}{c}2x-6+6=0+6\\ 2x=6\end{array}$

Divide each side by $2$ .

  $\begin{array}{c}\frac{2x}{2}=\frac{6}{2}\\ x=3\end{array}$

Now solve for $y$ . Subtract $4$ from each side of $y+4=0.$

  $\begin{array}{c}y+4-4=0-4\\ y=-4\end{array}$

Therefore, the value of $x$ is $3$ , and that of $y$ is $-4.$