|[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],...

`|[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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|(1+a^(2)-b^(2), 2ab, -2b),(2a, 1 -a^(2)+b^(2),2a),(2b, -2a, 1-a^2-b^2)|=(1 + a^2 + b^2)^(3) .

a) Prove that int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx" and evaluate "int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) b) Prove that |{:(1+a^(2)-b^(2), 2ab, -2b), (2ab, 1-a^(2)+b^(2), 2a), (2, -2a, 1-a^(2)-b^(2)):}|=(1+a^(2)+b^(2))^(3)

|[1, a, a^2-b c],[1,b, b^2-c a],[1,c, c^2-a b]|=

If a^2+b^2+c^2=0 and |(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)|=ka^2b^2c^2 , then the value of k is :

|(a^(2)+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|= 1 + a^2 + b^2 + c^2 .

If A= [[ab,b^2],[-a^2, -ab]] then A^(2)=

The determinant |(b^2-ab,b-c,-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2)| equals :

Subtract: 5a^2-7ab+5b^2 from 3ab-2a^2-2b^2

adj [[1,0,2],[-1,1,-2],[0,2,1]]= [[5,a,-2],[1,1,0],[-2,-2, b]] then (a, b)=

Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)

Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)
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Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)
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|[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...
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Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...
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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)
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|[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc
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Using properties of determinants, prove that |a+x y z x a+y z x y a+z...
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Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2...
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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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Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3
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Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y...
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Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^...
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Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...
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Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...
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IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...
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Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)
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Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...
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Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...
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Find the equation of the line joining A( 1,3) and B (0,0) using det...
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Using properties of determinants, prove the following: |xx+y x+2y\...
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