To solve the problem of finding the values of [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex] in the equation, we need to analyze the matrices given on both sides of the equation and equate their respective elements.
The given matrices are:
[tex]\[
\left[\begin{array}{rr}
-1 & -6 \\
9 & 3
\end{array}\right] = \left[\begin{array}{rr}
-1 & x \\
y & z
\end{array}\right]
\][/tex]
The elements of the matrices in corresponding positions must be equal. Let's match them element by element:
1. First row, first column:
[tex]\[
-1 = -1
\][/tex]
This equation is trivially satisfied.
2. First row, second column:
[tex]\[
-6 = x
\][/tex]
From this equation, we find:
[tex]\[
x = -6
\][/tex]
3. Second row, first column:
[tex]\[
9 = y
\][/tex]
From this equation, we find:
[tex]\[
y = 9
\][/tex]
4. Second row, second column:
[tex]\[
3 = z
\][/tex]
From this equation, we find:
[tex]\[
z = 3
\][/tex]
Thus, the values of the variables are:
[tex]\[
\begin{array}{l}
x = -6 \\
y = 9 \\
z = 3
\end{array}
\][/tex]
These results can be written as:
[tex]\[
\boxed{-6}
\][/tex]
[tex]\[
\boxed{9}
\][/tex]
[tex]\[
\boxed{3}
\][/tex]
