Multiply the Matrices [[2],[-3]][[9],[6]]

Problem

[[2],[−3]]*[[9,6]]

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 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: 2×9=18

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: 2×6=12

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: −3×9=−27

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: −3×6=−18

Final Answer

[[2],[−3]]*[[9,6]]=[[18,12],[−27,−18]]

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