Multiply the Matrices

Problem

[[4,4,3],[3,6,5],[3,0,2]]*[[294000],[414000],[162000]]

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 so the resulting matrix will be 3×1

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

4*(294000)+4*(414000)+3*(162000)

1176000+1656000+486000=3318000

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

3*(294000)+6*(414000)+5*(162000)

882000+2484000+810000=4176000

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

3*(294000)+0*(414000)+2*(162000)

882000+0+324000=1206000

Final Answer

[[4,4,3],[3,6,5],[3,0,2]]*[[294000],[414000],[162000]]=[[3318000],[4176000],[1206000]]

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