Simplify the Matrix

Problem

−6*[[1],[1],[3]]+9*[[−3],[4],[−6]]−15*[[2],[−2],[6]]

Solution

1. Perform scalar multiplication on each of the three vectors by multiplying every entry by the constant outside the brackets.

−6*[[1],[1],[3]]=[[−6],[−6],[−18]]

9*[[−3],[4],[−6]]=[[−27],[36],[−54]]

−15*[[2],[−2],[6]]=[[−30],[30],[−90]]

2. Add the resulting vectors by summing the corresponding components from each vector.

[[−6−27−30],[−6+36+30],[−18−54−90]]

3. Simplify the arithmetic for each row to find the final components.

−6−27−30=−63

−6+36+30=60

−18−54−90=−162

Final Answer

−6*[[1],[1],[3]]+9*[[−3],[4],[−6]]−15*[[2],[−2],[6]]=[[−63],[60],[−162]]

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