The determinant calculates the first line 1 21 - 1, the second line 1 0 - 20, the third line 3 21 - 1, the fourth line 1 23 4 The determinant calculates the first line 1 21 - 1, the second line 1 0 - 20, the third line 3 21 - 1, the fourth line 1 23 4

The determinant calculates the first line 1 21 - 1, the second line 1 0 - 20, the third line 3 21 - 1, the fourth line 1 23 4 The determinant calculates the first line 1 21 - 1, the second line 1 0 - 20, the third line 3 21 - 1, the fourth line 1 23 4

Determinant calculation of the first line 1 21 - 1, the second line 1 0 - 2 0, the third line 3 21 - 1, the fourth line 1 23 4 = - 401,2,1, - 11,0, - 2,03,2,1, - 11,2,3,4 = 1,2,1, - 11,0, - 2,02,0,0,01,2,3,4 = 2 * 2,1, - 10, - 2,02,3,4 = - 4 * 2, - 12,4 = - 4 * 10 = - 40

The first row is 1-102, the second row is 0-1-12, the third row is-12-10, and the fourth row is 211.0

r3+r1,r4-2r1
1 -1 0 2
0 -1 -1 2
0 1 -1 2
0 3 1 -4
r3+r2,r4+3r2
1 -1 0 2
0 -1 -1 2
0 0 -2 4
0 0 -2 2
r4-r3
1 -1 0 2
0 -1 -1 2
0 0 -2 4
0 0 0 -2
|A| = -4.

Solve the fourth-order determinant: the first line 2341, the second line 1031, the third line 2130, the fourth line 4215

Original formula = 2 × 0 × 3 × 5 + 1 × 1 × 1 × + 2 × 2 × 4 × 1 + 4 × 3 × 3 × 0-4 × 1 × 3 × 1-2 × 3 × 1 × 2-1 × 0 × 1 × 3-5 × 2 × 0 × 4 = 1 + 16-12-12 = - 7