Multiply the Matrices [[3],[4]]*[[-8],[6]]

Problem

[[3],[4]]*[[−8,6]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 2×1 column vector and the second matrix is a 1×2 row vector.

2. Determine the size of the resulting matrix. Since we are multiplying a 2×1 by a 1×2 the result will be a 2×2 matrix.

3. Apply the matrix multiplication rule where the element in row i and column j is the product of the ith row of the first matrix and the jth column of the second matrix.

4. Calculate the first row elements: 3×−8=−24 and 3×6=18

5. Calculate the second row elements: 4×−8=−32 and 4×6=24

Final Answer

[[3],[4]]*[[−8,6]]=[[−24,18],[−32,24]]

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