Simplify the Matrix

Problem

[[0.88,0],[0,0.85]]*[[36000,42000],[50000,58000]]

Solution

1. Identify the matrix multiplication rule for a 2×2 matrix multiplied by a 2×2 matrix, where the element in row i and column j is the dot product of row i of the first matrix and column j of the second.

2. Calculate the first row, first column entry by multiplying 0.88 by 36000 and 0 by 50000

0.88⋅36000+0⋅50000=31680

3. Calculate the first row, second column entry by multiplying 0.88 by 42000 and 0 by 58000

0.88⋅42000+0⋅58000=36960

4. Calculate the second row, first column entry by multiplying 0 by 36000 and 0.85 by 50000

0⋅36000+0.85⋅50000=42500

5. Calculate the second row, second column entry by multiplying 0 by 42000 and 0.85 by 58000

0⋅42000+0.85⋅58000=49300

6. Assemble the resulting values into the final matrix.

Final Answer

[[0.88,0],[0,0.85]]*[[36000,42000],[50000,58000]]=[[31680,36960],[42500,49300]]

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