Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+...

Prove that `| ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2abc(a+b+c)^3`

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Prove that ,,(b+c)^(2),a^(2),a^(2)b^(2),(c+a)^(2),b^(2)c^(2),c^(2),(a+b)^(2)]|=2abc(a+b+c)^(3)

Prove that: ,,(b+c)^(2),a^(2),a^(2)b^(2),(c+a)^(2),b^(2)c^(2),c^(2),(a+b)^(2)]|=2abc(a+b+c)^(3)

prove that |{:((b+c)^(2),,bc,,ac),(ba,,(c+a)^(2),,cb),(ca,,cb,,(a+b)^(2)):}| |{:((b+c)^(2),,a^(2),,a^(2)),(b^(2),,(c+a)^(2),,b^(2)),(c^(2),,c^(2),,(a+b)^(2)):}| =2abc (a+b+c)^(3)

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

Prove that |[(a+b)^(2),ca,bc],[ca,(b+c)^(2),ab],[bc,ab,(c+a)^(2)]|=2abc(a+b+c)^(3)

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

Prove that |{:(1,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(a+b+c)

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

Prove that |[a,b,c] , [a^2,b^2,c^2] , [a^3,b^3,c^3]|= abc(a-b)(b-c)(c-a)

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

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS

Find the value of k, if: |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k...
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If x,y and zinR, and Delta=|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x...
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If |(1,a^2,a^4),(1,b^2,b^4),(1,c^2,c^4)|=k|(1,1,1),(a,b,c),(a^2,b^2,c^...
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Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|
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|(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)...
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Using properties of determinants, prove that following: |"a"+"b"+2...
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|[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc
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Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...
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|(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))
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Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...
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Given A=[(0,-1,2),(2,-2,0)]andB-[(0,1),(1,0),(1,1)]. Find the product ...
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Using properties of determinants, solve the following for x: |x-2 ...
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FInd x when |[x+a, a^2, a^3] , [x+b, b^2, b^3] , [x+c, c^2, c^3]|=0 wh...
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Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...
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If x=-4 is a root of a Delta=|(x,2,3),(1,x,1),(3,2,x)|=0, then find th...
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Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...
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prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(...
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If f(x)=|a-1 0a x a-1a x^2a x a| , using properties of determinants...
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If A=[(2,-1,1),(-1,2,-1),(1,-1,2)] show that A^(2)-5A+4I=0 Hence fin...
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It A=[(-1,2,0),(-1,1,1),(0,1,0)] show that A^(2)=A^(-1)
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