Multiply the Matrices [[3,2],[-6,-7]][[-2],[4]]

Problem

[[3,2],[−6,−7]]*[[−2],[4]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×2 matrix and the second is a 2×1 matrix. The resulting matrix will be a 2×1 matrix.

2. Calculate the first element of the resulting matrix by taking the dot product of the first row of the left matrix and the column of the right matrix.

(3)*(−2)+(2)*(4)

3. Simplify the first element.

−6+8=2

4. Calculate the second element of the resulting matrix by taking the dot product of the second row of the left matrix and the column of the right matrix.

(−6)*(−2)+(−7)*(4)

5. Simplify the second element.

12−28=−16

6. Assemble the final matrix using the calculated values.

Final Answer

[[3,2],[−6,−7]]*[[−2],[4]]=[[2],[−16]]

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