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

Problem

[[2,−2,3]]*[[1],[−1],[2]]

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.

2. Determine the size of the resulting matrix. Since we are multiplying a 1×3 by a 3×1 the result will be a 1×1 matrix (a scalar).

3. Apply the dot product rule for matrix multiplication by multiplying corresponding elements and summing them.

2*(1)+(−2)*(−1)+3*(2)

4. Calculate the individual products.

2+2+6

5. Sum the values to find the final entry.

10

Final Answer

[[2,−2,3]]*[[1],[−1],[2]]=[(10)]

Want more problems? Check here!