Multiply the Matrices [[0.92,-0.33],[-0.46,0.66]][[2],[3]]

Problem

[[0.92,−0.33],[−0.46,0.66]]*[[2],[3]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 2×2 and the second is 2×1 resulting in a 2×1 matrix.

2. Calculate the first element of the resulting matrix by taking the dot product of the first row of the left matrix and the column of the right matrix.

0.92*(2)+(−0.33)*(3)

3. Simplify the arithmetic for the first element.

1.84−0.99=0.85

4. Calculate the second element of the resulting matrix by taking the dot product of the second row of the left matrix and the column of the right matrix.

−0.46*(2)+0.66*(3)

5. Simplify the arithmetic for the second element.

−0.92+1.98=1.06

6. Assemble the results into the final column matrix.

Final Answer

[[0.92,−0.33],[−0.46,0.66]]*[[2],[3]]=[[0.85],[1.06]]

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