|{:(" "1+a^2-b^2," "2ab," "-2b)...

`|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," "2a),(" "2b," "-2a,1-a^2-b^2):}|=(1+a^2+b^2)^3`

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The value of the determinant |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))| is equal to

By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: 2ab;1-a^2+b^2; 2a: 2b;-2a;1-a^2-b^2|=(1+a^2+b^2)^3

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

If a, b and c are in G.P. then prove that 1 a 2 - b 2 + 1 b 2 = 1 b 2 - c 2 . 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

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)) |:}

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

|{:(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 a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Factorise : 1-a^(2)+2ab-b^(2)

Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]| = 2(a-b)(b-c)(c-a)

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

solve |{:(x-2," "3," "3),(" "3,x+4," "5),(" "3," "5,x+4):}|=0
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show that x =2 is a root to the equation |{:(x,-6,-1),(2,-3x,x-3),(-...
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|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," ...
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|{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+a)^2," "b^2),(" "c^2," "c^2,(...
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Factorise : |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|
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|{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|
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If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...
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Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...
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Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...
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prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...
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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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