Multiply the Matrices [[5],[7]][[3],[-2]]

Problem

[[5],[7]]*[[3,−2]]

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 matrix by a 1×2 matrix, the result will be 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: 5⋅3=15

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: 5⋅(−2)=−10

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: 7⋅3=21

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: 7⋅(−2)=−14

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

Final Answer

[[5],[7]]*[[3,−2]]=[[15,−10],[21,−14]]

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