Find the Determinant

Problem

det(c)

Solution

1. Identify the matrix A and observe its row structure.

A=[[c,a,d,b],[a,c,d,b],[a,c,b,d],[c,a,b,d]]

2. Perform row operations to simplify the determinant. Subtract the second row from the first row ((R_1)→(R_1)−(R_2) and the third row from the fourth row ((R_4)→(R_4)−(R_3).

det(A)=det(c−a)

3. Observe that the first row and the fourth row are now identical.

(R_1)=[c−a,a−c,0,0]

(R_4)=[c−a,a−c,0,0]

4. Apply the property that if a matrix has two identical rows, its determinant is zero.

det(A)=0

Final Answer

det(c)=0

Want more problems? Check here!