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

Problem

[[2,−3,3]]*[[3],[−2],[1]]

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 the inner dimensions match (3), the product will be a 1×1 matrix (a scalar).

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

2*(3)+(−3)*(−2)+3*(1)

4. Calculate the individual products.

6+6+3

5. Sum the values to find the final entry.

15

Final Answer

[[2,−3,3]]*[[3],[−2],[1]]=[15]

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