Simplify the Matrix

Problem

[[−2,1,−2],[1,−1,2],[2,−1,1]]*[[9],[6],[−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 resulting matrix will be 3×1

2. Calculate the first element of the resulting matrix by taking the dot product of the first row of the matrix and the column vector.

(−2)*(9)+(1)*(6)+(−2)*(−9)=−18+6+18=6

3. Calculate the second element of the resulting matrix by taking the dot product of the second row and the column vector.

(1)*(9)+(−1)*(6)+(2)*(−9)=9−6−18=−15

4. Calculate the third element of the resulting matrix by taking the dot product of the third row and the column vector.

(2)*(9)+(−1)*(6)+(1)*(−9)=18−6−9=3

5. Combine the calculated elements into the final 3×1 matrix.

Final Answer

[[−2,1,−2],[1,−1,2],[2,−1,1]]*[[9],[6],[−9]]=[[6],[−15],[3]]

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