Big one determinant calculation problem! D= 1 1 1 1 a b c d a^2 b^2 c^2 d^2 a^4 b^4 c^4 d^4 The answer to this question is (a-b) (A-C) (A-D) (B-C) (B-D) (C-D) (a + B + C + D) If we want to use Vandermonde determinant in this problem! Why is there still no answer!

How to calculate the third (fourth) order determinant?
|a b c|
|d e f|
|g h i|
How to calculate?
What about the fourth order determinant?
|a b c d|
|e f g h |
|i j k l |
|m n o p|
By the way, is there a determinant of order 2 * 3? If so,
Hurry
I'm still in grade one
I'm not a little brother

Is there a determinant of order 2 * 3 like this? The answer is not. The one you said is matrix
These are collectively referred to as linear algebra. I learned it in the University. It's very simple
You don't need to know
I'll give you a general formula for their operation
I don't think you understand
Using N 2 elements AIJ (I, j = 1,2 , n)
|a11 a12 … a1n|
|a21 a22 … a2n|
| … … … … |
|an1 an2 … ann|
It represents the algebraic sum of the products of all n elements that may be taken from different rows and columns
The sign of each item is: when the row marks of the elements in this item are arranged in the order of natural numbers, if the arrangement of the corresponding column marks is even, then the sign is positive, and if it is odd, then the sign is negative. Therefore, the general term in the algebraic sum represented by the determinant of order n can be written as
(-1)^{N(j1j2… jn)}a1j1a2j2… anjn
such as
|a11 a12|
|a21 a22|
=a11a22-a12a21=∑(-1)^{N(j1j2)}*a1j1a2j2
I forgot to tell you
Arrange i1i2 at an n-level In, if there is a larger number it is before the smaller number is (is)

Fourth order determinant calculation, help!
Calculate the following fourth-order determinant
| 3 9 21 6 |
| 4 12 26 10 |
| 2 9 20 5 |
| -1 2 -7 7 |
Attached process 1 (I don't understand this step)
| 1 3 7 2 |
6 | 0 0 -1 1 |
| 0 3 6 1 |
| 0 5 0 9 |
And finally how to become the third-order determinant to the second-order determinant, please answer in detail ~ ~ requires a detailed process and explanation, high score reward, thank you~
PS, I just learned advanced algebra, the determinant of the solution process book is not detailed, especially the results of many 0, it is difficult to understand ~ you guys help me~
Why do you want to add the first line to the fourth line, and why do you want to move out the second double of the second line? I don't know much about it.

First, move out the three times of the first line, there is | 39 21 6 | = | 13 7 2 | 4 12 26 10 | 3 | 4 12 26 10 | 2 9 20 5 | | 29 20 5 | - 12 - 7 7 7 | - 12 - 7 7 7 | multiply the first line by - 4 and add to the second line: = | 1 3 7 2 | repeat as follows: multiply - 2 by - 2 and add to

1. Calculating determinant: 2 14 13 - 1 21 23 25 06 2

Expand the determinant by the fourth line,
The determinant d = (- 1) ^ 5 * 5 * 10 + (- 1) ^ 7 * 6 * (- 6) + (- 1) ^ 8 * 2 * 7 = - 50 + 36 + 14 = 0

Big one determinant calculation problem! D= 1 1 1 1 a b c d a^2 b^2 c^2 d^2 a^4 b^4 c^4 d^4 The answer to this question is (a-b) (A-C) (A-D) (B-C) (B-D) (C-D) (a + B + C + D) If we want to use Vandermonde determinant in this problem! Why is there still no answer!