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

Problem

[[−2,−3,2]]*[[3],[−2],[4]]

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. Since the number of columns in the first matrix matches the number of rows in the second, the result will be a 1×1 matrix (a single scalar value).

2. Apply the formula for matrix multiplication by calculating the dot product of the row and the column. Multiply corresponding elements and sum them.

(−2)*(3)+(−3)*(−2)+(2)*(4)

3. Multiply the individual terms.

−6+6+8

4. Simplify the expression by adding the results together.

0+8=8

Final Answer

[[−2,−3,2]]*[[3],[−2],[4]]=8

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