Simplify the Matrix -5[[4],[3],[-1]]

Problem

−5*[[4],[3],[−1]]

Solution

1. Identify the operation as scalar multiplication, where the scalar −5 is multiplied by each entry of the column vector.

2. Distribute the scalar −5 to the first element: −5⋅4=−20

3. Distribute the scalar −5 to the second element: −5⋅3=−15

4. Distribute the scalar −5 to the third element: −5⋅(−1)=5

5. Combine the results into a new column vector.

Final Answer

−5*[[4],[3],[−1]]=[[−20],[−15],[5]]

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