Question

Compute det b 4, where b = [2 4 1; 0 1 1; 1 2 1; 2 1 3; 5]

Answer 1

To compute the determinant of matrix b, perform row operations to simplify the matrix and then use the cofactor expansion method. The determinant of matrix b is 0.

Step-by-step explanation:

To compute the determinant of matrix b, you can perform row operations to simplify the matrix and then use the cofactor expansion method. Let's denote the matrix as [A], where A = [2 4 1; 0 1 1; 1 2 1; 2 1 3; 5].

Step 1: Swap rows R2 and R3 to create a leading 1 in the second row.

[A] = [2 4 1; 1 2 1; 0 1 1; 2 1 3; 5]

Step 2: Subtract 2 times row R3 from row R1 to create a leading zero in the first column of the first row.

[A] = [2 2 -1; 1 2 1; 0 1 1; 2 1 3; 5]

Step 3: Subtract 2 times row R3 from row R4 and subtract 5 times row R3 from row R5 to create zeros in the first column of the fourth and fifth rows.

[A] = [2 2 -1; 1 2 1; 0 1 1; 2 -3 1; 5 -9 0]

Step 4: Multiply the diagonal elements of the matrix.

det([A]) = 2 x 2 x 1 x (-3) x 0 = 0