Find values for the variables so that the following matrices are equal.
\[
\left[\begin{array}{rr}
x & 5 y \\
z & 3
\end{array}\right]=\left[\begin{array}{ll}
16 & 5 \\
17 & 3
\end{array}\right]
\]
\[
x=
\]
(Simplify your answer.)
Answer
\(\boxed{x = 16, y = 1, z = 17}\) are the solutions to the equations. Therefore, the values for the variables that make the two matrices equal are \(x = 16\), \(y = 1\), and \(z = 17\).
Step 1 ：Set up the following equations from the matrices: \(x = 16\), \(5y = 5\), and \(z = 17\).
Step 2 ：Solve the equations to find the values of x, y, and z.
Step 3 ：From \(x = 16\), we find that \(x = 16\).
Step 4 ：From \(5y = 5\), we can divide both sides by 5 to find that \(y = 1\).
Step 5 ：From \(z = 17\), we find that \(z = 17\).
Step 6 ：\(\boxed{x = 16, y = 1, z = 17}\) are the solutions to the equations. Therefore, the values for the variables that make the two matrices equal are \(x = 16\), \(y = 1\), and \(z = 17\).
