Simplify the Matrix [[6,10,-3]] , [[6],[(17-7)],[(-9+6)]]

Problem

[[6,10,−3]]*[[6],[17−7],[−9+6]]

Solution

1. Simplify the entries within the second matrix by performing the arithmetic operations.

17−7=10

−9+6=−3

2. Rewrite the matrix multiplication problem with the simplified values.

[[6,10,−3]]*[[6],[10],[−3]]

3. Apply the definition of matrix multiplication for a 1×3 row vector and a 3×1 column vector, which results in a 1×1 scalar.

(6⋅6)+(10⋅10)+(−3⋅−3)

4. Calculate the products of the individual terms.

36+100+9

5. Sum the results to find the final value.

36+100+9=145

Final Answer

[[6,10,−3]]*[[6],[17−7],[−9+6]]=145

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