Multiply the Matrices [[2,-1,3]][[1],[-2],[7]]

Problem

[[2,−1,3]]*[[1],[−2],[7]]

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.

2*(1)+(−1)*(−2)+3*(7)

3. Multiply the individual terms.

2+2+21

4. Simplify by adding the products together to find the final value.

25

Final Answer

[[2,−1,3]]*[[1],[−2],[7]]=25

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