Simplify the Matrix

Problem

[[12,16,8],[20,12,28],[32,28,36]]*[[220],[176],[264]]

Solution

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

2. Calculate the first element of the resulting matrix by multiplying the first row of the left matrix by the column vector.

12*(220)+16*(176)+8*(264)

2640+2816+2112=7568

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

20*(220)+12*(176)+28*(264)

4400+2112+7392=13904

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

32*(220)+28*(176)+36*(264)

7040+4928+9504=21472

5. Assemble the calculated values into the final column vector.

Final Answer

[[12,16,8],[20,12,28],[32,28,36]]*[[220],[176],[264]]=[[7568],[13904],[21472]]

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