Simplify the Matrix

Problem

[[0−24],[25−49],[50−74],[75−99],[100−124],[1245−149]]*[[4],[3],[6],[3],[5],[9]]

Solution

1. Simplify the subtractions inside the first matrix to find the numerical values of each element.

0−24=−24

25−49=−24

50−74=−24

75−99=−24

100−124=−24

1245−149=1096

2. Rewrite the problem as a multiplication of a 6×1 column vector and a 1×1 scalar, or interpret the juxtaposition as an element-wise multiplication if intended as a dot product of two vectors. Given the standard notation for a 6×1 matrix followed by another 6×1 matrix without a transpose, this is interpreted as the Hadamard (element-wise) product.

3. Multiply corresponding entries from the two matrices.

−24⋅4=−96

−24⋅3=−72

−24⋅6=−144

−24⋅3=−72

−24⋅5=−120

1096⋅9=9864

Final Answer

[[0−24],[25−49],[50−74],[75−99],[100−124],[1245−149]]*[[4],[3],[6],[3],[5],[9]]=[[−96],[−72],[−144],[−72],[−120],[9864]]

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