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CBSE CLASS XII

Determinants

Q. 1. Prove that 

 = (1- x3)2

Q. 2. Find the equation of the line joining A(1,3) and B(0,0) using determinants and find  if D (K, 0) is a point such that area of a triangle ABD is 3 square units.

Q. 3. If 

A =    Verify that A³ – 6A² + 9A – 4I = 0 and hence find A^-1

Q. 4. Prove that :

  = (1 – x2)

Q. 5. Solve by matrix method:
2x + y + z = 1
= 3/2
5z = 9

Q. 6. Prove that :
 = a³

Q. 7. Prove that :

= abc + bc + ca + ab.

Q. 8. Solve :

= 0

Q. 9. Using determinants, find the area of the triangle whose vertices are (1, 4), (2, 3), (-5, 3). Are the given points collinear.

Q. 10. If the points (a₁, b₁),  (a₂, b₂) and (a₁ + a₂ b₁ + b₂) are collinear, Show that a1b2 = a2b1.

Q. 11. If a, b, c are all positive and are p^th , q^th and r^th terms of G.P., then show that
D = = 0

Q. 12. If

= 0, then Prove that
a, b, c are in G.P  or  x, y, z are in G.P

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed., M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962