QuestionEvaluate the matrix expression: 2⎣⎡−564−8−7−1⎦⎤+⎣⎡−285−9−26⎦⎤−⎣⎡52−95−10⎦⎤ Simplify the resulting matrix.
Studdy Solution
STEP 1
Assumptions1. We are given three matrices and we need to perform operations on them.
. The operations are addition and multiplication by a scalar. 3. The matrices are of the same size, so the operations are valid.
STEP 2
First, we need to multiply the first matrix by the scalar2. We do this by multiplying each element in the matrix by2. 2⎣⎡−564−8−7−1⎦⎤=⎣⎡2(−5)2(6)2(4)2(−8)2(−7)2(−1)⎦⎤
STEP 3
Calculate the result of the multiplication. ⎣⎡2(−5)2(6)2()2(−8)2(−7)2(−1)⎦⎤=⎣⎡−10128−16−14−2⎦⎤
STEP 4
Now we have three matrices that we can add and subtract. We do this by adding or subtracting the corresponding elements in the matrices. ⎣⎡−10128−16−14−2⎦⎤+⎣⎡−28−9−26⎦⎤−⎣⎡2−9−10⎦⎤=⎣⎡−10−2−12+8−28++9−16−9−−14−2+1−2+6−0⎦⎤
STEP 5
Calculate the result of the addition and subtraction. ⎣⎡−10−2−512+8−28+5+9−16−9−5−14−2+1−2+−0⎦⎤=⎣⎡−171822−30−154⎦⎤The resulting matrix is⎣⎡−171822−30−154⎦⎤
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