Pregunta
The matrices shown below must be equal to each other. \[ \left[\begin{array}{cc}x & 2 y \\ z & 9\end{array}\right]=\left[\begin{array}{cc}4 & 12 \\ 3 & 9\end{array}\right] \] Find the value of each variable and enter it in the relevant box provided below: \( x= \) \( y= \) \( z= \)
Ask by Osborne Cummings. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( x=4 \), \( y=6 \), \( z=3 \)
Solución
To ensure the two matrices are equal, we set the corresponding elements equal to each other:
\[
\begin{cases}
x = 4 \\
2y = 12 \\
z = 3 \\
9 = 9 \quad (\text{This confirms the bottom-right elements are already equal})
\end{cases}
\]
Solving for \( y \):
\[
2y = 12 \implies y = \frac{12}{2} = 6
\]
**Final Values:**
\[
x = 4
\]
\[
y = 6
\]
\[
z = 3
\]
**Answer:**
\( x=4 \)
\( y=6 \)
\( z=3 \)
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Simplifique esta solución Extra Insights
To find the values of \( x \), \( y \), and \( z \), we can set the corresponding elements of the two matrices equal to each other: 1. The first element: \( x = 4 \) 2. The second element: \( 2y = 12 \) → Dividing both sides by 2 gives \( y = 6 \) 3. The third element: \( z = 3 \) 4. The fourth element: \( 9 = 9 \) is already satisfied. Now, we have the values: \( x = 4 \) \( y = 6 \) \( z = 3 \)
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