Perform the indicated operations.$-2\left(\begin{bmatrix}3&-6\\5&-7\\12&8\end{bmatrix}+\begin{bmatrix}6&9\\-8&1\\10&-3\end{bmatrix}\right)=$−2([3 −65 −712 8]+[6 9−8 110 −3])=
Question
Perform the indicated operations.−2([3 −65 −712 8]+[6 9−8 110 −3])=
Solution
First, we need to add the two matrices together.
The sum of the two matrices is:
[3+6, -6+9] [5-8, -7+1] [12+10, 8-3]
which simplifies to:
[9, 3] [-3, -6] [22, 5]
Then, we multiply this resulting matrix by -2:
-2*[9, 3] -2*[-3, -6] -2*[22, 5]
which gives us the final matrix:
[-18, -6] [6, 12] [-44, -10]
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