Multiply the Matrices

Problem

[[2,2,0],[−4,−3,2],[0,−3,−5]]*[[−10],[2],[−9]]

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 result will be a 3×1 matrix.

2. Calculate the first element by taking the dot product of the first row of the left matrix and the column of the right matrix.

(2)*(−10)+(2)*(2)+(0)*(−9)=−20+4+0=−16

3. Calculate the second element by taking the dot product of the second row of the left matrix and the column of the right matrix.

(−4)*(−10)+(−3)*(2)+(2)*(−9)=40−6−18=16

4. Calculate the third element by taking the dot product of the third row of the left matrix and the column of the right matrix.

(0)*(−10)+(−3)*(2)+(−5)*(−9)=0−6+45=39

Final Answer

[[2,2,0],[−4,−3,2],[0,−3,−5]]*[[−10],[2],[−9]]=[[−16],[16],[39]]

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