Finding the fourth order determinant 1234 / 2341 / 3412 / 4123 There should be process and method! It doesn't matter

Finding the fourth order determinant 1234 / 2341 / 3412 / 4123 There should be process and method! It doesn't matter

1 2 3 42 3 4 13 4 1 24 1 2 3=1*[3*(1*3-2*2)-4*(4*3-2*1)+1*(4*2-1*1)]-2*[2*(1*3-2*2)-4*(3*3-2*4)+1*(3*2-1*4)]+3*[2*(4*3-2*1)-3*(3*3-2*4)+1*(3*1-4*4)]-4*[2*(4*2-1*1)-3*(3*2-1*4)+4*(3*1-4*4)]=1*(-3-40+7)...

How to calculate the first line 1234, the second line 2341, the third line 3412 and the fourth line 4123 of the fourth order determinant

Step 1: add columns 2, 3 and 4 to column 1, propose the common factor 10 of column 1, and change it into
1 2 3 4
1 3 4 1
1 4 1 2
1 1 2 3
Step 2: multiply the first line by - 1 and add it to the other lines
1 2 3 4
0 1 1 -3
0 2 -2 -2
0 -1 -1 -1
Step 3: R3 - 2r1, R4 + R1
1 2 3 4
0 1 1 -3
0 0 -4 4
0 0 0 -4
So determinant = 10 * (- 4) * (- 4) = 160

The fourth order determinant | a | = 1234 / 4123 / 3412 / 2341, find ∑ 4, k = 1, ∑ 4, j = 1aij
|A|=1 2 3 4
4 1 2 3
3 4 1 2
2 3 4 1
Shouldn't AIJ be a complement? Why is it still level 4?

This is the sum of the algebraic cofactors of all the elements of | a |
It's a lot of trouble
There are two ways:
1. Calculate a * = |a|a ^ - 1 and add up all the elements of a *
2. Replace the i-th line of | a | with four 1s, calculate the determinant, and get the sum of the algebraic cofactors of the i-th line elements of A
I = 1,2,3,4, which requires four fourth-order determinants
It is suggested to use method 1 to calculate a determinant | a | = - 160, and use elementary row transformation to change (a, e) into (E, a ^ - 1) to get a ^ - 1=
-9/40 11/40 1/40 1/40
1/40 -9/40 11/40 1/40
1/40 1/40 -9/40 11/40
11/40 1/40 1/40 -9/40
So a *=
36 -44 -4 -4
-4 36 -44 -4
-4 -4 36 -44
-44 -4 -4 36
The results show that ∑ AIJ = - 64

(1234＋2341＋3412＋4123)÷(1＋2＋3＋4)

Thousand bits = (1 + 2 + 3 + 4) / (1 + 2 + 3 + 4) = 10 / 10 = 1
One hundred and ten are the same
So the answer is 1111
The original formula is 11110 △ 10 = 1111

375 plus 0. 683 minus 1 and 3 / 8

2.375+0.683-11/8
=3.058-11/8
=3.058-1.375
=1.683

2.46 times 1.1 minus 1.71 simple algorithm 8.37 times 0.2 plus 8.37 times 8 plus 8.37 times 1.8 simple algorithm

=2.46+0.246-1.71=2.706-1.71=0.996
=8.37*(8+0.2+1.8)=8.37*10=83.7

120 divided by [45 times (1 minus 8 / 9)]

120 divided by [45 times (1 minus 8 / 9)]
=120÷[45x(1-8/9)]
=120÷(45x1/9）
=120÷5
=24
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What is 16 = what, 9 = 0.375, what divided by 40 = what

6:16=9/24=0.375=3÷8=37.5%

6 / () = 0.375 = 9; () = 40 parts () = ()%

Hello!
6 / (16) = 0.375 = 9; (24) = 15 out of 40 = (37.5)%
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() 8 = 0.375 = nine parts = (): 40 = ()%

(3) 8 = 0.375 = 9 / 24 = (15): 40 = (37.5)%