Multiply the Matrices [[0.9,0.3],[0.1,0.7]]*[[21000],[18000]]

Problem

[[0.9,0.3],[0.1,0.7]]*[[21000],[18000]]

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 multiplying the first row of the first matrix by the column of the second matrix.

0.9⋅21000+0.3⋅18000

18900+5400=24300

3. Calculate the second element of the resulting matrix by multiplying the second row of the first matrix by the column of the second matrix.

0.1⋅21000+0.7⋅18000

2100+12600=14700

4. Combine the results into the final column matrix.

Final Answer

[[0.9,0.3],[0.1,0.7]]*[[21000],[18000]]=[[24300],[14700]]

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