If x, y, z are different and Delta=|xx^2...

If x, y, z are different and `Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0`, then

Text Solution

Verified by Experts

The correct Answer is:

`0`

Topper's Solved these Questions

DETERMINANTS
NCERT GUJARATI|Exercise EXERCISE 4.1|8 Videos
DETERMINANTS
NCERT GUJARATI|Exercise EXERCISE 4.2|16 Videos
CONTINUITY AND DIFFERENTIABILITY
NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos
DIFFERENTIAL EQUATIONS
NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}| =0 then show that 1+xyz=0

If x , y , z are all different real numbers, then 1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2

If x, y, z are in A.P. and tan^(-1)x , tan^(-1)y and t a n^(-1)z are also in A.P., then (1) 2x""=""3y""=""6z (2) 6x""=""3y""=""2z (3) 6x""=""4y""=""3z (4) x""=""y""=""z

If x,y and z are three real numbers such that x+y+z=4 and x^2+y^2+z^2=6 ,then show that each of x,y and z lie in the closed interval [2/3,2]

If x,y,z are all different from zero and |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=0 then value of x^(-1)+y^(-1)+z^(-1) is ".........."

Using properties of determinants in Exercise 11 to 15 prove that |{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)

x≥0,y≥0,z≥0 and tan^(-1) x+tan^(-1) y+tan^(-1) z=k , the possible value(s) of k if x^2 + y^2+z^2 = 1, & \ x+y+z=sqrt(3) , then

The point of intersecting of the line passing through (0, 0, 1) and intersecting the lines x+2y+z=1, -x+y-2z=2 and x+y=2, x+z=2 with xy-plane is

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them : (a) 7x + 5y + 6z + 30 = 0 and 3x - y-10z + 4 = 0 (b) 2x + y + 32 - 2 = 0 and x - 2y + 5 = 0 (c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z-1 = 0 (d) 2x – y + 3z-1 = 0 and 2x - y + 3z + 3 = 0 (e) 4x + 8y + z - 8 = 0 and y + z - 4 = 0

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4

If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=...
Text Solution
|
Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...
Text Solution
|
Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...
Text Solution
|
Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...
Text Solution
|
If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...
Text Solution
|
Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0
Text Solution
|
Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...
Text Solution
|
If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...
Text Solution
|
Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|
Text Solution
|
Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|
Text Solution
|
Using peoperties of determinants in questions 11 to 15, prove that : ...
Text Solution
|
Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...
Text Solution
|
Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...
Text Solution
|
Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.
Text Solution
|
Without expanding, show that the value of each of the determinants is ...
Text Solution
|
Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...
Text Solution
|
Choose the correct answer in questions 17 to 19: If a, b, c are in ...
Text Solution
|
Choose the correct answer in questions 17 to 19: If x, y, z are non...
Text Solution
|
Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...
Text Solution
|