Multiply the Matrices [[30,55],[30,50],[20,15]]*[[25],[6]]

Problem

[[30,55],[30,50],[20,15]]*[[25],[6]]

Solution

1. Identify the dimensions of the matrices to ensure they can be multiplied. The first matrix is 3×2 and the second is 2×1 so the resulting matrix will be 3×1

2. Calculate the first element of the product by multiplying the first row of the first matrix by the column of the second matrix.

30⋅25+55⋅6=750+330=1080

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

30⋅25+50⋅6=750+300=1050

4. Calculate the third element by multiplying the third row of the first matrix by the column of the second matrix.

20⋅25+15⋅6=500+90=590

5. Assemble the results into the final 3×1 matrix.

Final Answer

[[30,55],[30,50],[20,15]]*[[25],[6]]=[[1080],[1050],[590]]

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