Multiply the Matrices [[6,-3,4]][[5],[2],[-6]]

Problem

[[6,−3,4]]*[[5],[2],[−6]]

Solution

1. Identify the dimensions of the matrices. The first matrix is a 1×3 row vector and the second matrix is a 3×1 column vector. The resulting matrix will be a 1×1 scalar.

2. Apply the formula for matrix multiplication by calculating the dot product of the row and the column. This involves multiplying corresponding elements and summing the results.

3. Multiply the corresponding elements:

6⋅5=30

−3⋅2=−6

4⋅−6=−24

4. Sum the products to find the final value:

30+(−6)+(−24)=0

Final Answer

[[6,−3,4]]*[[5],[2],[−6]]=[0]

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