Multiply the Matrices

Problem

[[31,−34,−31],[−66,−106,19],[−60,−76,46]]*[[4],[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 and the column vector.

(31)*(4)+(−34)*(2)+(−31)*(8)=124−68−248=−192

3. Calculate the second entry by taking the dot product of the second row and the column vector.

(−66)*(4)+(−106)*(2)+(19)*(8)=−264−212+152=−324

4. Calculate the third entry by taking the dot product of the third row and the column vector.

(−60)*(4)+(−76)*(2)+(46)*(8)=−240−152+368=−24

Final Answer

[[31,−34,−31],[−66,−106,19],[−60,−76,46]]*[[4],[2],[8]]=[[−192],[−324],[−24]]

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