Multiply the Matrices [[5],[-2],[1]][[2],[3],[-1]]

Problem

[[5],[−2],[1]]*[[2,3,−1]]

Solution

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

2. Determine the size of the resulting matrix. Multiplying a 3×1 matrix by a 1×3 matrix results in a 3×3 matrix.

3. Apply the matrix multiplication rule where each element (c_i*j) is the product of the ith row of the first matrix and the jth column of the second matrix.

4. Calculate the first row:

5×2=10

5×3=15

5×−1=−5

5. Calculate the second row:

−2×2=−4

−2×3=−6

−2×−1=2

6. Calculate the third row:

1×2=2

1×3=3

1×−1=−1

Final Answer

[[5],[−2],[1]]*[[2,3,−1]]=[[10,15,−5],[−4,−6,2],[2,3,−1]]

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