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. Multiplying a 2×1 matrix by a 1×2 matrix results in a 2×2 matrix.

3. Calculate the entry at row 1, column 1 by multiplying the first element of the first matrix by the first element of the second matrix.

3⋅(−8)=−24

4. Calculate the entry at row 1, column 2 by multiplying the first element of the first matrix by the second element of the second matrix.

3⋅6=18

5. Calculate the entry at row 2, column 1 by multiplying the second element of the first matrix by the first element of the second matrix.

4⋅(−8)=−32

6. Calculate the entry at row 2, column 2 by multiplying the second element of the first matrix by the second element of the second matrix.

4⋅6=24

7. Assemble the results into the final 2×2 matrix.

Final Answer

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

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