Multiply the Matrices

Problem

[[−3,0,1],[5,−7,5],[1,0,−3]]*[[−3],[−6],[−3]]

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.

(−3)*(−3)+(0)*(−6)+(1)*(−3)=9+0−3=6

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)*(−3)+(−7)*(−6)+(5)*(−3)=−15+42−15=12

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)*(−3)+(0)*(−6)+(−3)*(−3)=−3+0+9=6

Final Answer

[[−3,0,1],[5,−7,5],[1,0,−3]]*[[−3],[−6],[−3]]=[[6],[12],[6]]

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