Multiply the Matrices

Problem

[[8,−1,0],[7,5,−4],[3,2,9]]*[[3],[2],[−8]]

Solution

1. Identify the dimensions of the matrices. The first matrix is 3×3 and the second is 3×1 so the resulting matrix will be 3×1

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.

(8)*(3)+(−1)*(2)+(0)*(−8)=24−2+0=22

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.

(7)*(3)+(5)*(2)+(−4)*(−8)=21+10+32=63

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.

(3)*(3)+(2)*(2)+(9)*(−8)=9+4−72=−59

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

Final Answer

[[8,−1,0],[7,5,−4],[3,2,9]]*[[3],[2],[−8]]=[[22],[63],[−59]]

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