Multiply the Matrices 2[[4],[-1],[3]]*(3[[2],[5],[-7]])

Problem

2*[[4],[−1],[3]]⋅(3*[[2],[5],[−7]])

Solution

1. Apply scalar multiplication to each vector by multiplying every entry by the constant outside the brackets.

2*[[4],[−1],[3]]=[[8],[−2],[6]]

3*[[2],[5],[−7]]=[[6],[15],[−21]]

2. Identify the operation as the dot product (inner product) of two vectors, since both are represented as column vectors in the expression.

[[8],[−2],[6]]⋅[[6],[15],[−21]]

3. Calculate the dot product by multiplying corresponding components and summing the results.

(8)*(6)+(−2)*(15)+(6)*(−21)

4. Simplify the arithmetic to find the final scalar value.

48−30−126=−108

Final Answer

2*[[4],[−1],[3]]⋅(3*[[2],[5],[−7]])=−108

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