Find the Determinant of the Resulting Matrix

Problem

[[1,9,−3],[5,4,3],[−2,9,8]]*[[−4],[8],[2]]

Solution

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

2. Multiply the matrices by calculating the dot product of each row of the first matrix with the column vector.

3. Calculate the first element:

(1)*(−4)+(9)*(8)+(−3)*(2)=−4+72−6=62

4. Calculate the second element:

(5)*(−4)+(4)*(8)+(3)*(2)=−20+32+6=18

5. Calculate the third element:

(−2)*(−4)+(9)*(8)+(8)*(2)=8+72+16=96

6. Determine the determinant of the resulting 3×1 matrix. The determinant is only defined for square matrices (matrices with the same number of rows and columns).

7. Conclude that because the resulting matrix is a 3×1 matrix and not a square matrix, the determinant does not exist.

Final Answer

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

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