It is known that the equations 2x-3 = m and 3x-2 = 2m have the same root, so we can find the value of M

It is known that the equations 2x-3 = m and 3x-2 = 2m have the same root, so we can find the value of M

The solution of equation 2x-3 = m is x = 3 + m2, the solution of equation 3x-2 = 2m is x = 2m + 23, then 3 + M2 = 2m + 23 is m = 5

To calculate the determinant, the first line is 1-231, the second line is 2-314, the third line is 3201, and the fourth line is 01152

r2-2r1,r3-3r1
1 -2 3 1
0 1 -5 2
0 8 -6 -2
0 1 5 2
r3-8r2,r4-r1
1 -2 3 1
0 1 -5 2
0 0 36 -18
0 0 10 0
R3 - (36 / 10) R4, r3r4 (Note: determinant multiplied by - 1)
1 -2 3 1
0 1 -5 2
0 0 10 0
0 0 0 -18
So determinant = (- 1) * 10 * (- 18) = 180

How to calculate the fourth-order determinant. The first line is 4,1,1,1, the second line is 1,4,1,1, the third line is 1,1,4,1, and the fourth line is 1,1,1,4

D =
c1+c2+c3+c4
7 1 1 1
7 4 1 1
7 1 4 1
7 1 1 4
r2-r1,r3-r1,r4-r1
7 1 1 1
0 3 0 0
0 0 3 0
0 0 0 3
= 7*3*3*3
= 189

Calculate a fourth-order determinant! The first row a 100, the second row - 1 B 10, the third row 0 - 1 C 1, the fourth row 0 0 - 1 D

It can't be simplified. Just use the expansion formula directly. Because there are many zero values in the determinant, you can see that there are only two terms after expansion
One is the positive diagonal (subscript: 11, 22, 33, 44, value is ABCD), the other is the reverse (subscript: 12, 21, 34, 43, value is - 1). So the determinant value is: ABCD - 1
I hope it will help you