Simplify the Matrix 3[[4],[3],[-1]]+4[[9],[2],[4]]

Problem

3*[[4],[3],[−1]]+4*[[9],[2],[4]]

Solution

1. Perform scalar multiplication on the first vector by multiplying each component by 3

3*[[4],[3],[−1]]=[[12],[9],[−3]]

2. Perform scalar multiplication on the second vector by multiplying each component by 4

4*[[9],[2],[4]]=[[36],[8],[16]]

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

[[12],[9],[−3]]+[[36],[8],[16]]=[[12+36],[9+8],[−3+16]]

4. Simplify the arithmetic to find the final vector components.

[[48],[17],[13]]

Final Answer

3*[[4],[3],[−1]]+4*[[9],[2],[4]]=[[48],[17],[13]]

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