Add (-2)[[3],[2]]+(5)[[-4],[1]]

Problem

−2*[[3],[2]]+5*[[−4],[1]]

Solution

1. Perform scalar multiplication on the first vector by multiplying each component by −2

−2*[[3],[2]]=[[−6],[−4]]

2. Perform scalar multiplication on the second vector by multiplying each component by 5

5*[[−4],[1]]=[[−20],[5]]

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

[[−6],[−4]]+[[−20],[5]]=[[−6+(−20)],[−4+5]]

4. Simplify the components to find the final vector.

[[−6−20],[−4+5]]=[[−26],[1]]

Final Answer

−2*[[3],[2]]+5*[[−4],[1]]=[[−26],[1]]

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