|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b...

`|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2):}|=4a^2b^2c^2`

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Evalute |{:(0,c,b),(c,0,a),(b,a,0):}| and hence show that, |{:(" "-a^2," "ab," "ac),(" "ab," "-b^2," "bc),(" "ca," "bc," "-c^2):}|=4a^2b^2c^2

If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lambdaa^2b^2c^2, then find the value of lambda

Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}| , hence show that . |{:(0,c,b),(c,0,a),(b,a,0):}|^2=|{:(b^2+c^2," "ab," "ac),(" "ab,c^2+a^2," "bc),(" "ca," "bc,a^2+b^2):}|=4a^2b^2c^2

Prove that {:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2)

Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c^2 .

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

prove that, |{:(""-bc ,b^2+bc,c^2+bc),(a^2+ac," "-ac,c^2+ac),(a^2+ab,b^2+ab," "-ab):}|=(ab+bc+ca)^3

Using the property of determinants and without expanding {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...
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|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc
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|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...
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|{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...
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|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)
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|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3
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|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
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|{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...
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|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
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|{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...
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prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...
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If a ,b ,c are in A.P , show that , |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+...
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If A,B,C , are the angles of a triangles, show that, |{:(sin^2A,coaA,1...
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without expanding prove that [22-24] |{:(7,12,-3),(9,14,-1),(8,13,-2...
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|{:(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b)):}|=0
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|{:(logx xyz,logxy,logxz),(logyxyz,1,logyz),(logzxyz,logzy,1):}|=0
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if |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam...
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|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" ...
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Show that |{:(x-3,x-4,x-alpha),(x-2,x-3,x-beta),(x-1,x-2,x-gamma):}|=0...
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If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c...
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