The product of all values of t , for whi...

The product of all values of `t ,` for which the system of equations `(a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0` has non-trivial solution, is `|a-c-b-c b-a-b-a c|` (b) `|a b c b c a c a b|` `|a c bb a cc b a|` (d) `|a a+bb+c bb+cc+a cc+a a+b|`

`|{:(a,-c,-b),(-c,b,-a),(-b,-a,c),(-b,-a,c):}|`

`|{:(a,b,c),(b,c,a),(c,a,b):}|`

`|{:(a,c,b),(b,a,c),(c,b,a):}|`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

DETERMINANT
FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level -II|19 Videos
DETERMINANT
FIITJEE|Exercise COMPREHENSIONS -I|3 Videos
DETERMINANT
FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level -II|12 Videos
DEFINITE INTEGRAL
FIITJEE|Exercise NUMERICAL BASED|3 Videos
ELLIPSE
FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If a!=b!=c!=1 and the system of equations ax+y+z=0,x+by+z=0 ,x+y+cz=0 have non trivial solutions then a+b+c-abc

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

If the system of equations ax + by + c = 0,bx + cy +a = 0, cx + ay + b = 0 has infinitely many solutions then the system of equations (b + c) x +(c + a)y + (a + b) z = 0(c + a) x + (a+b) y + (b + c) z = 0(a + b) x + (b + c) y +(c + a) z = 0 has

The system of linear equations x + y + z = 0 (2x)/(a) + (3y)/(b) + (4z)/(c ) = 0 (x)/(a) + (y)/(b) + (z)/(c ) = 0 has non trivia solution then

If a+b+c!=0, the system of equations (b+c)(y+z)-ax=b-c,(c+a)(z+x)-by=c-a and (a+b)(x+y)-cz=a-b has

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

If the system of linear equations a(y+z)-x=0,b(z+x)-y=0,c(x+y)-z=0 has a non trivial solution,(a!=-1,b!=-1,c!=-1), then show that (1)/(1+a)+(1)/(1+b)+(1)/(1+c)=2

FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I

If f(x)=|{:(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x...
Text Solution
|
The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-s...
Text Solution
|
The system of equation 102x-95y+88z=81,3x+10y+17z=24, 57x+50y+43z=36 h...
Text Solution
|
IF ax^3+bx^2+cx+d=|(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), ...
Text Solution
|
In a Delta ABC |[1,1,1],[1+sinA,1+sinB,1+sinC][sinA+sin^2A,sinB+sin^2B...
Text Solution
|
If a,b,c are sides of a triangle and |(a^(2),b^(2),c^(2)),((a+1)^(2),(...
Text Solution
|
The value of |(.^(10)C(4).^(10)C(5).^(11)C(m)),(.^(11)C(6).^(11)C(7).^...
Text Solution
|
If D=|{:(2,1,[sin^2theta]),([sin^2theta],costheta,i),(i,1,sintheta):}|...
Text Solution
|
If alpha is a root of x^4 = 1 with negative principal argument then th...
Text Solution
|
If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1...
Text Solution
|
Let x1y1z1,x2y2z2 and x3y3z3 be three 3-digit even numbers and Delta=|...
Text Solution
|
If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0, then th...
Text Solution
|
The product of all values of t , for which the system of equations (a-...
Text Solution
|
Let a,b,c , in R not all are equal and Delta(1)= |{:(a,,b,,c),(b,,c,...
Text Solution
|
The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...
Text Solution
|
If Delta (x)=|{:(x,1+x^(2),x^(3)),(log(1+x^(2)),e^(x),sinx),(cosx,tanx...
Text Solution
|
If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...
Text Solution
|
Statement 1: The product of two diagonal matrices of order 3 is also ...
Text Solution
|
Statement -1 : If Delta(x)=|{:(f1(x),f2(x),f3(x)),(a2,b2,c2),(a3,b3,c3...
Text Solution
|
Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...
Text Solution
|