Find the Determinant

Problem

det(x)

Solution

1. Identify the matrix and choose a row or column for expansion. Expanding along the second column is most efficient because it contains two zeros.

2. Apply the cofactor expansion formula along the second column. The sign pattern for the second column is negative, positive, negative.

3. Calculate the determinant by multiplying the non-zero entry 2*x by its corresponding cofactor. The entry 2*x is in the third row, second column, so its sign is negative.

D=−(2*x)*det(x)

4. Evaluate the 2×2 determinant using the formula a*d−b*c

det(x)=(x)*(−1/(x2))−(1)*(1/x)

5. Simplify the expression inside the parentheses.

(x)*(−1/(x2))−1/x=−1/x−1/x

−1/x−1/x=−2/x

6. Multiply the result by the external factor −(2*x)

−(2*x)*(−2/x)=(4*x)/x

(4*x)/x=4

Final Answer

det(x)=4

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