Find the Determinant of the Resulting Matrix

Problem

[[i+2,5*i+5,−3*i−2],[−1,−i−3,i+1],[0,−1,1]]*[[13+i],[−4−i],[−5]]

Solution

1. Identify the dimensions of the matrices to determine the shape of the resulting matrix.

2. Observe that the first matrix is a 3×3 matrix and the second is a 3×1 column vector.

3. Recall that the product of a 3×3 matrix and a 3×1 matrix results in a 3×1 matrix.

4. Note that the determinant is only defined for square matrices (matrices where the number of rows equals the number of columns).

5. Conclude that since the resulting matrix is a 3×1 column vector and not a square matrix, the determinant cannot be calculated.

Final Answer

The determinant is undefined for non-square matrices.

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