if Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(...

if `Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0` then

`(y - 2z + 3x)^(2)`

`(x - 2y + z)^(2)`

`(x + y + z)^(2)`

`x^(2) + y^(2) + z^(2) - zy - yz - zx`

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Let |{:(y^(5)z^(6)(z^(3)-y^(3)),,x^(4)z^(6)(x^(3)-z^(3)),,x^(4)y^(5)(y^(3)-x^(3))),(y^(2)z^(3)(y^(6)-z^(6)),,xz^(3)(z^(6)-x^(6)) ,,xy^(2)(x^(6)-y^(6))),(y^(2)^(3)(z^(3)-y^(3)),,xz^(3)(x^(3)-z^(3)),,xy^(2)(y^(3)-x^(3))):}| " and " Delta_(2)= |{:(x,,y^(2),,z^(3)),(x^(4),,y^(5) ,,z^(6)),(x^(7),,y^(8),,z^(9)):}| .Then Delta_(1)Delta_(2) is equal to

If x,y,z in R and |{:(x,y^2,z^3),(x^4,y^5,z^6),(x^7,y^8,z^9):}|=2 then find the value of |{:(y^5z^6(z^3-y^3),x^4z^6(x^3-z^3),x^4y^5(y^3-x^3)),(y^2z^3(y^6-z^6),xz^3(z^6-x^6), xy^2(x^6-y^6)),(y^2z^3(z^3-y^3),xz^3(x^3-z^3),xy^2(y^3-x^3)):}|

If x,y,z in R & Delta =|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x+3y,9x+7y+3z)|=-16 then the value of x is

If [{:(,x-y,1,z),(,2x-y,0,w):}]=[{:(,-1,1,4),(,0,0,5):}], "find x,y,z,w"

find the values of x,y and zfrom the following equations : (i) [{:(4,3),(x,5):}]=[{:(y,z),(1,5):}] (ii) [{:(x+y,2),(5+z,xy):}]=[{:(6,2),(5,8):}] (iii) [{:(x+y+z),(x+z),(y+z):}]=[{:(9),(5),(7):}]

If A = [(5, -1, 4), (2, 3, 5), (5, -2, 6)] , find A^(-1) and use it to solve the following system of equation 5x - y + 4z = 5, 2x + 3y +5z = 2, 5x - 2y + 6z =-1

The coordinates of the point of intersection of the lines (x-1)/1=(y+2)/3=(z-2)/(-2) with the plane 3x+4y+5z-25=0 is (A) (5,6,-10) (B) (5,10,-6) (C) (-6,5,10) (D) (-6,10,5)

If A=[{:(9, 7, 3), (5, -1, 4), (6, 8, 2):}]" find "A^(-1) and hence solve the system of equations: 9x+7y+3z=6, 5x-y+4z=1, 6x+8y+2z=4 .

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise

For positive numbers x, y and z, the numerical value of the determinan...
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Calculate the value of the determinant |{:(1,1,1,1),(1,2,3,4),(1,3,6,1...
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if Delta= |{:(3,,4,,5,,x),(4,,5,,6,,y),(5,,6,,7,,z),(x,,y,,z,,0):}|=0 ...
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If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...
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If a,b,and c are the side of a triangle and A,B and C are the angles o...
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If [ ] denotes the greatest integer less than or equal to the real num...
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The coefficicent of x in f(x) =|{:(x,1+sinx,cosx),(1, log(1+x),2),(x^2...
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The determinant |(cos C,tan A,0),(sin B,0,-tan A),(0,sin B,cos C)| h...
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Using the factor theorem it is found that a+b , b+ca n dc+a are three ...
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The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)|, is
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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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The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,...
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The value of the determinant Delta = |((1 - a(1)^(3) b(1)^(3))/(1 - ...
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The determinant Delta = |(b,c,b alpha +c),(c,d,c alpha + d),(b alpha...
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Delta = |(1//a,1,bc),(1//b,1,ca),(1//c,1,ab)|=
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If |(1 +ax,1 +bx,1 + bx),(1 +a(1) x,1 +b(1) x,1 + c(1) x),(1 + a(2) x,...
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If abc!=0 then |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| is
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If 1 + (1)/(a) + (1)/(b) + (1)/(c) = 0, then Delta = |(1 +a,1,1),(1,...
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If a, b and c are all different from zero and Delta = |(1 +a,1,1),(1...
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In a Delta ABC, a, b, c are sides and A, B, C are angles opposite to t...
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