Find the Variables [[a],[b]]=[[4,2],[-2,1]][[-2],[2]]

Problem

[[a],[b]]=[[4,2],[−2,1]]*[[−2],[2]]

Solution

1. Identify the matrix multiplication operation, where a 2×2 matrix is multiplied by a 2×1 column vector.

2. Calculate the first component a by taking the dot product of the first row of the matrix and the column vector.

a=(4)*(−2)+(2)*(2)

3. Simplify the expression for a

a=−8+4

a=−4

4. Calculate the second component b by taking the dot product of the second row of the matrix and the column vector.

b=(−2)*(−2)+(1)*(2)

5. Simplify the expression for b

b=4+2

b=6

Final Answer

[[a],[b]]=[[−4],[6]]

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