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Problem

a*[[−2],[−4],[1],[1]]+b*[[3],[−4],[0],[4]]+d*[[−1],[−12],[2],[6]]

Solution

1. Distribute the scalars a b and d into each component of their respective vectors.

a*[[−2],[−4],[1],[1]]=[[−2*a],[−4*a],[a],[a]]

b*[[3],[−4],[0],[4]]=[[3*b],[−4*b],[0],[4*b]]

d*[[−1],[−12],[2],[6]]=[[−d],[−12*d],[2*d],[6*d]]

2. Add the corresponding components of the three resulting vectors to form a single vector.

[[−2*a+3*b−d],[−4*a−4*b−12*d],[a+0+2*d],[a+4*b+6*d]]

3. Simplify the expressions within each row of the vector.

[[−2*a+3*b−d],[−4*a−4*b−12*d],[a+2*d],[a+4*b+6*d]]

Final Answer

a*[[−2],[−4],[1],[1]]+b*[[3],[−4],[0],[4]]+d*[[−1],[−12],[2],[6]]=[[−2*a+3*b−d],[−4*a−4*b−12*d],[a+2*d],[a+4*b+6*d]]

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