Multiply the Matrices [[0,-2,3]]*[[0],[-2],[1]]

Problem

[[0,−2,3]]*[[0],[−2],[1]]

Solution

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

2. Apply the dot product formula for matrix multiplication. Multiply each corresponding element from the row of the first matrix and the column of the second matrix, then sum the products.

3. Calculate the individual products.

0⋅0=0

(−2)⋅(−2)=4

3⋅1=3

4. Sum the results to find the final value.

0+4+3=7

Final Answer

[[0,−2,3]]*[[0],[−2],[1]]=[7]

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