Multiply the Matrices

Problem

[[−3−1,0,2],[2,−1−1,−1],[−4,0,−3−1]]*[[x],[y],[z]]

Solution

1. Simplify the entries within the first matrix by performing the subtractions.

[[−4,0,2],[2,−2,−1],[−4,0,−4]]*[[x],[y],[z]]

2. Apply the matrix multiplication rule by multiplying each row of the first matrix by the column vector.

[[(−4)*(x)+(0)*(y)+(2)*(z)],[(2)*(x)+(−2)*(y)+(−1)*(z)],[(−4)*(x)+(0)*(y)+(−4)*(z)]]

3. Simplify the resulting expressions to obtain the final vector.

[[−4*x+2*z],[2*x−2*y−z],[−4*x−4*z]]

Final Answer

[[−3−1,0,2],[2,−1−1,−1],[−4,0,−3−1]]*[[x],[y],[z]]=[[−4*x+2*z],[2*x−2*y−z],[−4*x−4*z]]

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