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Problem

[[1,0,−3],[4,−6,2]]+3*[[7,−4,2],[1,−4,−3]]

Solution

1. Distribute the scalar 3 to every element in the second matrix.

[[3*(7),3*(−4),3*(2)],[3*(1),3*(−4),3*(−3)]]

2. Simplify the multiplication within the second matrix.

[[21,−12,6],[3,−12,−9]]

3. Add the corresponding elements of the first matrix and the newly scaled second matrix.

[[1+21,0+(−12),−3+6],[4+3,−6+(−12),2+(−9)]]

4. Calculate the final sums for each position in the matrix.

[[22,−12,3],[7,−18,−7]]

Final Answer

[[1,0,−3],[4,−6,2]]+3*[[7,−4,2],[1,−4,−3]]=[[22,−12,3],[7,−18,−7]]

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