For x ne y ne z , |{:(1+x^(3),,x^(2),,...

For `x ne y ne z , |{:(1+x^(3),,x^(2),,1),(1+y^(3),,y^(2),,1),(1+z^(3),,z^(2),,1):}|=0 ` if xyz is

`-2`

`-1`

`-3`

none of these

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If xneynez" and " |{:(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3)):}|=0, then xyz =

if x ne 0 , y ne 0 ,z ne 0 " and " |{:(1+x,,1,,1),(1+y,,1+2y,,1),(1+z,,1+z,,1+3z):}|=0 then x^(-1) +y^(-1) +z^(-1) is equal to

Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}| =(x-y)(y-z)(z-x)(x+y+z)

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

Using properties of determinats prove that : |(x,x(x^(2)+1),x+1),(y,y(y^(2)+1),y+1),(z,z(z^(2)+1),z +1)|=(x-y)(y-z)(z-x)(x+y+z)

Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(z-x)(x+y+z)

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

If [(1,0,0),(0, 0, 1),(0,1,0)][(x),(y),(z)]=[(2),(-1),(3)] , find x ,\ y ,\ z .

proof |[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]| = |[1,1,1],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise

Let Delta(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4m-2),((a-1)^(3),3n^(3)...
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if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...
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For x ne y ne z , |{:(1+x^(3),,x^(2),,1),(1+y^(3),,y^(2),,1),(1+z^(3...
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" if " |{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a...
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If A is a square matrix of order n such that its elements are polynomi...
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Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),...
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a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...
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If alpha,beta,gamma are real numbers, then without expanding at any...
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If A,B,C are the angles of triangle ABC, then the minimum value of |{:...
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If x, y , z are in A.P., then the value of the det (A) is , where A ...
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Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...
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If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...
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Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...
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Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2
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Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...
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If B is a non-sinfular matrix and A is square matrix, then det B^(-1)A...
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If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...
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If the determinant |(b -c,c -a,a -b),(b' -c',c' -a',a' -b'),(b'' -c'',...
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If a !=b, then the system of equation ax + by + bz = 0 bx + ay + bz ...
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if |{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}|= (a-b)(b-c)(c-a)(a+...
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