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Prove that: |{:(a, b, c), (x, y, z), (...

Prove that: `|{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|`

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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}|=2|{:(a,p,x),(b,q,y),(c,r,z):}|

Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]| = |[a,b,c],[x,y,z],[yz,zx,yx]|

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Let Delta=|{:(a,p,x),(b,q,y),(c,r,z):}|=16" then "Delta_1=|{:(p+x,a+x,a+p),(q+y,b+y,b+q),(r+z,c+z,c+r):}|=32

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If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........

ALLEN -DETERMINANTS-All Questions
  1. The value of |{:(1, 2, 3),(-4, 3, 6), (2,-7, 9):}| is a. 213 b.-231 ...

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  2. Find the minors and cofactors of elements '-3^(prime),\ \ ^(prime)5^(p...

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  3. Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, ...

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  4. Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a...

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  5. If |3^2+k4^2 3^2+3+k4^2+k5^2 4^2+4+k5^2+k6^2 5^2+5+k|=0 then the value...

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  6. Prove that abs((a,a,x),(m,m,m),(b,x,b))=m(x-a)(x-b)

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  7. Let alpha "and " beta be the roots of the equation ax^(2)+bx+c=0. Let ...

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  8. Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha...

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  9. Find the nature of solution for the given system of equation: x+2y+3...

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  10. If the following equations x+y-3 = 0, (1+lamda)x + (2+lamda) y - 8 = 0...

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  11. If the system of equation x+lambday+1=0,\ lambdax+y+1=0\ &\ x+y+lambda...

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  12. The value of determinant |a-bb-cc-a b-cc-a a-b c-a a-bb-c| is equal to...

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  13. Solve the following integration int (3 sin x cos^(2)x-sin^(3)x)dx

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  14. The value of the determinant |{:(-a, b, c), (a,-b, c), (a, b,-c):}| is...

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  15. For any "Delta"A B C the value of determinant |sin^2\ \ A cot A1sin^2B...

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  16. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

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  17. If A+B+C=pi,\ t h e n\ |"sin"(A+B+C) sinB cosC -sinB 0 tanA "cos"(A+B)...

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  18. The number of real values of x satisfying |(x,3x+2,2x-1),(2x-1,4x,3x+1...

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  19. If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then...

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  20. If a1, a2 an ,\ a(n+1) are in GP and a1>0AAI ,\ t h e n |loganloga(n+2...

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