The first behavior of the third-order determinant is 1 A, 1,1, the second behavior is 1,1 B, 1, and the third behavior is 1,1,1 C. find the value of this determinant

The first behavior of the third-order determinant is 1 A, 1,1, the second behavior is 1,1 B, 1, and the third behavior is 1,1,1 C. find the value of this determinant

Can't you type the "+" sign? | 1 + a 1 1 | = | 1 + a 1 1 | = | 1 + A + A / B + A / C 1 1 | [Note: C1 + C2 * A / B + C3 * A / C] 1 1 1 + B 1 - a B 00 B 01 1 + C - a 0 C 00 C = (1 + A + A / B + A / C) * BC = BC + ABC + AC + AB = ABC + AB + BC + Ca

Equation determinant = 0, find x
1 1 1 …… one
1 a1 a2 a3…… an
1 a1² a2² a3²…… an²
……………………
1 a1na2n a3²n…… ann
corrections:
determinant
1 1 1 …… one
1 a1 a2 a3…… an
1 a1² a2² a3²…… an²
……………………
x a1^n a2^n a3^n…… an^n
It's zero
Find x

Write x as 1 + (x-1), the determinant is divided into two D = Π (AI-1) Π (AJ AI) + (- 1) ^ (n + 1 + 1) (x-1) Π (AJ AI) = [Π (AI-1) + (- 1) ^ n (x-1)] Π (AJ AI), so when A1,..., an are different, Π (AI-1) + (- 1) ^ n (x-1) = 0, so x = 1 + (- 1) ^ n Π (AI-1)

Finding the root of determinant equation f (x) = 0

r2-2r1,r3+r4
Determinant = (omitted)
Expand by line 2
Then press line 3 to expand
f(x)= k (x^2-9)(x^2-1)
So x = plus or minus 3, plus or minus 1