Home
Class 12
MATHS
The value of the determinant |k a k^2+a^...

The value of the determinant `|k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1|` is `k(a+b)(b+c)(c+a)` `k a b c(a^2+b^(f2)+c^2)` `k(a-b)(b-c)(c-a)` `k(a+b-c)(b+c-a)(c+a-b)`

A

`k(a+b)(b+c)(c+a)`

B

`k abc (a^(2)+b^(2)+c^(2))`

C

`k(a-b)(b-c)(c-a)`

D

`k(a+b-c)(b+c-a)(c+a-b)`

Text Solution

Verified by Experts

The correct Answer is:
C
we have
`|{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2),,1),(kc,,k^(2)+c^(2),,1):}|=|{:(ka,,k^(2),,1),(kb,,k^(2),,1),(kc,,k^(2),,1):}|+|{:(ka,,a^(2),,1),(kb,,b^(2),,1),(kc,,c^(2),,1):}|`
`=0+k |{:(a,,a^(2),,1),(b,,b^(2),,1),(c,,c^(2),,1):}|`
`=k(a-b) (b-c) (c-a)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)| is (A) k(a+b)(b+c)(c+a) (B) k a b c(a^2+b^(2)+c^2) (C) k(a-b)(b-c)(c-a) (D) k(a+b-c)(b+c-a)(c+a-b)

What is the value of k, if |{:(k,b+c,b^(2)+c^(2)),(k,c+a,c^(2)+a^(2)),(k,a+b,a^(2)+b^(2)):}|=(a-b)(b-c)(c-a) ?

What is the value of k, if |(k,b+c,b^(2)+c^(2)),(k,c+a,c^(2) + a^(2)),(k,a+b,a^(2)+b^(2))| = (a - b) (b - c) (c - a) ?

The determinant a^(2)(a+b),ab,acab,b^(2)(a+k),bcac,bc,c^(2)(1+k)]|

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

In A B C ,(a+b+c)(b+c-a)=k b c if k 0 = 4