Multiply the Matrices [[20,45],[25,50],[20,10]]*[[15],[9]]

Problem

[[20,45],[25,50],[20,10]]*[[15],[9]]

Solution

1. Identify the dimensions of the matrices to ensure multiplication is possible. The first matrix is 3×2 and the second is 2×1 The resulting matrix will be 3×1

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

20⋅15+45⋅9=300+405=705

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

25⋅15+50⋅9=375+450=825

4. Calculate the third element by multiplying the third row of the left matrix by the column of the right matrix.

20⋅15+10⋅9=300+90=390

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

Final Answer

[[20,45],[25,50],[20,10]]*[[15],[9]]=[[705],[825],[390]]

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