|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c...

`|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=`

abc

`(a-b)(b-c)(c-a)`

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Without expanding the determinant, prove that (i) |{:(a,a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}| (ii) |{:(ax,by,cz),(x^(2),y^(2),z^(2)),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}| (iii) |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

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Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

If bc+ca+ab=18 , and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=lambda|(1,1,1),(a,b,c),(a^(2),b^(2),c^(2))| the value of lambda is

|(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab)|=

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AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II

If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta...
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|(1,log(x)y,log(x)z),(log(y)x,1,log(y)z),(log(z)x,log(z)y,1)|=
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|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=
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Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...
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If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...
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If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...
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If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|
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|(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|
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Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...
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If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=
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If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...
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Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}...
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If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then
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If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(...
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If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0
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If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...
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If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=...
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If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...
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If |(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z)|=64 then x=
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If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...
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