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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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: - \( x = 16 \) - \( y = 4 \) - \( z = 13 \)

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- \( x = 16 \) - \( y = 4 \) - \( z = 13 \)
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