Multiply the Matrices

Problem

[[−3,0,1],[−5,3,−5],[1,0,−3]]*[[1],[2],[1]]

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 entry by taking the dot product of the first row of the left matrix and the column of the right matrix.

(−3)*(1)+(0)*(2)+(1)*(1)=−3+0+1=−2

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

(−5)*(1)+(3)*(2)+(−5)*(1)=−5+6−5=−4

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

(1)*(1)+(0)*(2)+(−3)*(1)=1+0−3=−2

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

Final Answer

[[−3,0,1],[−5,3,−5],[1,0,−3]]*[[1],[2],[1]]=[[−2],[−4],[−2]]

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