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

Problem

[[−1],[1],[1]]*[[−2,0,−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. Each element (c_i*j) in the resulting matrix is the product of the ith row of the first matrix and the jth column of the second matrix.

4. Calculate the elements of the first row:

(−1)*(−2)=2

(−1)*(0)=0

(−1)*(−1)=1

5. Calculate the elements of the second row:

(1)*(−2)=−2

(1)*(0)=0

(1)*(−1)=−1

6. Calculate the elements of the third row:

(1)*(−2)=−2

(1)*(0)=0

(1)*(−1)=−1

Final Answer

[[−1],[1],[1]]*[[−2,0,−1]]=[[2,0,1],[−2,0,−1],[−2,0,−1]]

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