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Show that Delta={:|(x,p,q),(p,x,q),(q,q,...

Show that `Delta={:|(x,p,q),(p,x,q),(q,q,x)| = (x-p)(x^2+px-2q^2)`

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Compute : {:[(p,q),(q,p)]+[(p,q),(-q,p)]

Using the property of determinants and without expanding 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,x),(c,r,z)|

Without expanding prove that |(a,b,c),(x,y,z),(p,q,r)| = |(y,b,q),(x,a,p),(z,c,r)|

Show that: |[p-q-r,2p,2p],[2q,q-r-p,2q],[2r,2r,r-p-q]|=(p+q+r)^3

Using the properties of determinant, show that : |[1,p+q,p^2+q^2],[1,q+r,q^2+r^2],[1,r+p,r^2+p^2]| = (p-q)(q-r)(r-p)

Using the properties of determinants show that : |[[p^2, q^2, r^2],[qr,rp,pq],[p,q,r]]|=(p-q)(q-r)(r-p)(pq+qr+rp)

Show that: (9p – 5q)^2 + 180pq = (9p + 5q)^2

Find the condition that the st. lines : p_1x+q_1y=1,p_2x+q_2y=1 and p_3x+q_3y=1 be concurrent, show that the point (p_1,q_1),(p_2,q_2) and (p_3,q_3) are collinear.

Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1-x^2)|[a,c,p],[b,d,q],[u,v,w]|

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of...

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  2. Find area of the triangle with vertices at the point given in the fol...

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  3. Show that Delta={:|(x,p,q),(p,x,q),(q,q,x)| = (x-p)(x^2+px-2q^2)

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  4. If Delta= {:|(0,b-a,c-a),(a-b,0,c-b),(a-c,b-c,0)|, then show that Delt...

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  5. If x = -4 is a root of Delta= {:|(x,2,3),(1,x,1),(3,2,x)|=0, then find...

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  6. Show that the points (a+5,a-4),(a-1,a+3) and (a,a) do not lie on a str...

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  7. If A=[(3,1),(7,5)] , find x and y so that A^2 + xI-yA=0. Hence find A^...

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  8. Without expanding, show that the following determinants vanish: {:|(...

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  9. Prove that: {:|(a+b+nc,na-a,nb-b),(nc-c,b+c+na,nb-b),(nc-c,na-a,c+a+...

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  10. Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1...

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  11. If |[[x,2],[18,x]]|=|[[6,2],[18,6]]|, then x is equal to:

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  12. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  13. Which of the following is correct

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  14. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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  15. Let A be a non-singular matrix of order 3 xx 3. Then I adj. A I is equ...

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  16. Select the Correct Option If A is an invertible matrix of order 2, the...

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  17. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  18. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

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  19. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

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  20. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

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