Add 3[[1],[-3]]+2[[2],[4]]

Problem

3*[[1],[−3]]+2*[[2],[4]]

Solution

1. Distribute the scalar 3 into the first vector by multiplying it with each component.

3*[[1],[−3]]=[[3*(1)],[3*(−3)]]=[[3],[−9]]

2. Distribute the scalar 2 into the second vector by multiplying it with each component.

2*[[2],[4]]=[[2*(2)],[2*(4)]]=[[4],[8]]

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

[[3],[−9]]+[[4],[8]]=[[3+4],[−9+8]]

4. Simplify the arithmetic to find the final vector.

[[3+4],[−9+8]]=[[7],[−1]]

Final Answer

3*[[1],[−3]]+2*[[2],[4]]=[[7],[−1]]

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