If a , b , c are non-zero, then the syst...

If `a , b , c` are non-zero, then the system of equations `(alpha+a)x+alphay+alphaz=0,alphax+(alpha+b)y+alphaz=0,alphax+alphay+(alpha+c)z=0` has a non-trivial solution if `alpha^(-1)=-(a^(-1)+b^(-1)+c^(-1))` b. `alpha^(-1)=a+b+c` c.`alpha+a+b+c=1` d. none of these

`alpha^(-1) = - (a^(-1) + b^(-1) +c^(-1))`

`alpha^(-1) = a + b + c`

`alpha + a + b + c = 1`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DETERMINANTS
DISHA PUBLICATION|Exercise EXERCISE -1 CONCEPT BUILDER|65 Videos
CONTINUITY AND DIFFERENTIABILITY
DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
DIFFERENTIAL EQUATIONS
DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

If a,b,are non-zeroes then the system of equations (alpha+a)x+alpha y+alpha z=0alpha x+(alpha+b)y+alpha z=0alpha x+alpha y+(alpha+c)z=0

If a,b,c are non-zero,then the system of equations (alpha+a)x+alpha y+alpha z=0,alpha x+(alpha+b)y+alpha z=0,alpha x+alpha y+(alpha+c)z=0 has a non-trivial solution if alpha^(-1)=(A)-(a^(-1)+b^(-1)+c^(-1))(B)a+b+c (C) alpha+a+b+c=1 (D) none of these

The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 x+y+alphaz=alpha-1 and has no solution if alpha is

The system of equations ax+by+(a alpha+ b)z=0 bx+cy+(b alpha+c)z=0 (a alpha+b)x+(balpha+c)y=0 has a non zero solutions if a,b,c are in

Given that a alpha^(2)+2b alpha+c!=0 and that the system of equations (a alpha+b)x+alpha y+bz=0,(b alpha+c)x+by+cz=0,(a alpha+b)y+(b alpha+c)z=0 has a non trivial solution,then a ,b,c are in

The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1, x+y+alphaz=alpha-1 has no solution if alpha is (A) 1 (B) not -2 (C) either -2 or 1 (D) -2

The value of |alpha| for which the system of equation alphax+y+z=alpha-1 x+alphay+z=alpha-1 x+y+alphaz=alpha-1 has no solution , is "____"

DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR

If [] denotes the greatest integer less than or equal to the real numb...
Text Solution
|
Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...
Text Solution
|
If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...
Text Solution
|
If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...
Text Solution
|
If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...
Text Solution
|
If omega is a non-real cube root of unity, then Delta = |(a(1) + b(1) ...
Text Solution
|
prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...
Text Solution
|
Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....
Text Solution
|
If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...
Text Solution
|
The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...
Text Solution
|
The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...
Text Solution
|
If a^(2)+b^(2)+c^(2)=-2 and |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((...
Text Solution
|
If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...
Text Solution
|
If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...
Text Solution
|
If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...
Text Solution
|
the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...
Text Solution
|
f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...
Text Solution
|
If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then
Text Solution
|
If the system of linear equations x1 + 2x2 + 3x3 = 6, x1 + 3x2 + 5x3 =...
Text Solution
|
If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...
Text Solution
|