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The determinant |(a^(2)+10,ab, ac),(ab...

The determinant
`|(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)+10)|` is

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

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

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)) |:}

Show that, |{:(a^2+10,ab,ac),(ab,b^2+10,bc),(ca,bc,c^2+10):}| is divisible by 100 .

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)

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

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)= (a) A (b) B (c) I (d) A^(2)+B^(2)

If D=|(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)| , then D is -

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

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  2. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

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  3. The determinant |(a^(2)+10,ab, ac),(ab, b^(2)+10, bc),(ac, bc, c^(2)...

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  4. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of det...

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  5. If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 10...

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  6. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

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  7. Let f(n)=|n n+1 n+2 ^n Pn^(n+1)P(n+1)^n Pn^n Cn^(n+1)C(n+1)^(n+2)C(n+2...

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  8. If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]...

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  9. Let x<1, then value of |[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]| is...

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  10. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

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  11. Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...

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  12. If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...

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  13. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

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  14. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

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  15. Let f(x)=a(5)x^(5)+a(4)x^(4)+a(3)x^(3)+a(2)x^(2)+a(1)x, "where" a(i),s...

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  16. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

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  17. Roots of the equation |x m n1a x n1a b x1a b c1|)=0 are independent ...

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  18. Prove that the value of each the following determinants is zero: |[a...

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  19. If a ,b ,c are different, then the value of x satisfying |[0,x^2-a, x^...

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  20. Prove that the value of each the following determinants is zero: |...

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