We need to find the values of the variables [tex]\( m \)[/tex], [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex] such that the given matrices are equal. Let's compare corresponding elements from both matrices step-by-step.
We start with the first row:
[tex]\[
\begin{array}{ccc}
-7 & -7 & x \\
\end{array}
\][/tex]
must equal
[tex]\[
\begin{array}{ccc}
-7 & m+4 & 4 \\
\end{array}
\][/tex]
From the first element:
[tex]\[
-7 = -7
\][/tex]
This equation is already satisfied; no variable here.
From the second element:
[tex]\[
-7 = m + 4
\][/tex]
Solving for [tex]\( m \)[/tex]:
[tex]\[
m = -7 - 4 \implies m = -11
\][/tex]
From the third element:
[tex]\[
x = 4
\][/tex]
Now, let's move to the second row:
[tex]\[
\begin{array}{ccc}
0 & 6 & y+4 \\
\end{array}
\][/tex]
must equal
[tex]\[
\begin{array}{ccc}
0 & 6 & 5 \\
\end{array}
\][/tex]
From the first element:
[tex]\[
0 = 0
\][/tex]
This equation is already satisfied; no variable here.
From the second element:
[tex]\[
6 = 6
\][/tex]
This equation is already satisfied; no variable here.
From the third element:
[tex]\[
y + 4 = 5
\][/tex]
Solving for [tex]\( y \)[/tex]:
[tex]\[
y = 5 - 4 \implies y = 1
\][/tex]
Finally, let's look at the third row:
[tex]\[
\begin{array}{ccc}
-6 & -5 & z \\
\end{array}
\][/tex]
must equal
[tex]\[
\begin{array}{ccc}
-6 & -5 & -1 \\
\end{array}
\][/tex]
From the first element:
[tex]\[
-6 = -6
\][/tex]
This equation is already satisfied; no variable here.
From the second element:
[tex]\[
-5 = -5
\][/tex]
This equation is already satisfied; no variable here.
From the third element:
[tex]\[
z = -1
\][/tex]
Therefore, the values that satisfy the given matrix equation are:
[tex]\[
m = -11, \quad x = 4, \quad y = 1, \quad z = -1
\][/tex]
Thus, the statement can be true if [tex]\( m = -11 \)[/tex], [tex]\( x = 4 \)[/tex], [tex]\( y = 1 \)[/tex], and [tex]\( z = -1 \)[/tex].
