Multiply the Matrices [[4],[-3]][[1],[2]]

Problem

[[4],[−3]]*[[1,2]]

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: 4×1=4

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: 4×2=8

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: −3×1=−3

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: −3×2=−6

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

Final Answer

[[4],[−3]]*[[1,2]]=[[4,8],[−3,−6]]

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