Barrett Munoz
08/13/2024 · Junior High School
ix operations Perform the indicated matrix operations. \( \left[\begin{array}{ccc}3 & 6 & 3 \\ 2 & 2 & -2 \\ -1 & -4 & 0\end{array}\right]+3\left[\begin{array}{ccc}-2 & -2 & 2 \\ -2 & 2 & 2 \\ 2 & 2 & -2\end{array}\right] \)
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Tutor-Verified Answer
Step-by-step Solution
To solve this matrix addition problem, we need to perform the following steps:
1. Multiply the second matrix by 3.
2. Add the resulting matrix to the first matrix.
Let's start with the multiplication:
\( 3 \times \left[\begin{array}{ccc}-2 & -2 & 2 \\ -2 & 2 & 2 \\ 2 & 2 & -2\end{array}\right] = \left[\begin{array}{ccc}-6 & -6 & 6 \\ -6 & 6 & 6 \\ 6 & 6 & -6\end{array}\right] \)
Now, let's add this result to the first matrix:
\( \left[\begin{array}{ccc}3 & 6 & 3 \\ 2 & 2 & -2 \\ -1 & -4 & 0\end{array}\right] + \left[\begin{array}{ccc}-6 & -6 & 6 \\ -6 & 6 & 6 \\ 6 & 6 & -6\end{array}\right] \)
To add the matrices, we add the corresponding elements:
\( \left[\begin{array}{ccc}3 + (-6) & 6 + (-6) & 3 + 6 \\ 2 + (-6) & 2 + 6 & -2 + 6 \\ -1 + 6 & -4 + 6 & 0 + (-6)\end{array}\right] \)
This simplifies to:
\( \left[\begin{array}{ccc}-3 & 0 & 9 \\ -4 & 8 & 4 \\ 5 & 2 & -6\end{array}\right] \)
So, the result of the matrix operation is:
\( \left[\begin{array}{ccc}-3 & 0 & 9 \\ -4 & 8 & 4 \\ 5 & 2 & -6\end{array}\right] \)
Quick Answer
The result of the matrix operation is \( \left[\begin{array}{ccc}-3 & 0 & 9 \\ -4 & 8 & 4 \\ 5 & 2 & -6\end{array}\right] \).
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