Simplify the Matrix (-4)[[1],[-4],[1]]+(2)[[3],[1],[6]]

Problem

−4*[[1],[−4],[1]]+2*[[3],[1],[6]]

Solution

1. Perform scalar multiplication on the first vector by multiplying each entry by −4

−4*[[1],[−4],[1]]=[[−4],[16],[−4]]

2. Perform scalar multiplication on the second vector by multiplying each entry by 2

2*[[3],[1],[6]]=[[6],[2],[12]]

3. Add the resulting vectors by summing the corresponding components.

[[−4],[16],[−4]]+[[6],[2],[12]]=[[−4+6],[16+2],[−4+12]]

4. Simplify the arithmetic for each entry.

[[2],[18],[8]]

Final Answer

−4*[[1],[−4],[1]]+2*[[3],[1],[6]]=[[2],[18],[8]]

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