Find the Determinant [[1,2,1],[0,1,2],[0,-1,0]]

Problem

det(1)

Solution

1. Identify the matrix and choose a method for expansion. Since the first column contains two zeros, expanding along the first column is the most efficient approach.

2. Apply the cofactor expansion formula along the first column. The determinant is the sum of the elements in the column multiplied by their corresponding cofactors.

det(A)=(a_11)⋅(C_11)+(a_21)⋅(C_21)+(a_31)⋅(C_31)

3. Substitute the values from the first column. Since (a_21)=0 and (a_31)=0 only the first term remains.

det(A)=1⋅det(1)−0+0

4. Calculate the determinant of the 2×2 minor matrix using the formula a*d−b*c

det(1)=(1)*(0)−(2)*(−1)

5. Simplify the arithmetic to find the final value.

0−(−2)=2

Final Answer

det(1)=2

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