Find the Determinant of the Resulting Matrix [[3,0,2],[2,-1,3],[7,1,3]][[u],[v],[w]]

Problem

det([[3,0,2],[2,−1,3],[7,1,3]]*[[u],[v],[w]])

Solution

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

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

3. Apply the definition of the determinant. The determinant is only defined for square matrices (where the number of rows equals the number of columns).

4. Conclude that because the resulting matrix is a 3×1 matrix and not a square matrix, the determinant cannot be calculated.

Final Answer

The determinant is undefined for a non-square *3×1* matrix.

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