Garza Reed
04/23/2024 · Senior High School
Find values tor the \( \left.\begin{array}{ll}x & 7 y \\ z & 4\end{array}\right]=\left[\begin{array}{cc}16 & 28 \\ 13 & 4\end{array}\right] \) \( x=16 \) (Simplify your answer.) \( y=4 \) (Simplify your answer.) \( z=\square \) (Simplify your answer)
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Tutor-Verified Answer
Step-by-step Solution
To solve for the values of \( x \), \( y \), and \( z \) in the matrix equation
\[
\left[\begin{array}{cc} x & 7y \\ z & 4 \end{array}\right] = \left[\begin{array}{cc} 16 & 28 \\ 13 & 4 \end{array}\right],
\]
we can equate the corresponding elements of the two matrices.
1. From the first row, first column:
\[
x = 16.
\]
2. From the first row, second column:
\[
7y = 28.
\]
To find \( y \), we divide both sides by 7:
\[
y = \frac{28}{7} = 4.
\]
3. From the second row, first column:
\[
z = 13.
\]
4. From the second row, second column:
\[
4 = 4,
\]
which is already satisfied.
Thus, the values are:
- \( x = 16 \)
- \( y = 4 \)
- \( z = 13 \)
So, the final answers are:
- \( x = 16 \)
- \( y = 4 \)
- \( z = 13 \)
Quick Answer
- \( x = 16 \)
- \( y = 4 \)
- \( z = 13 \)
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