Match the following
Column-IColumn-II(i) Let |A| = |aij|3×3 ≠ 0. Eachelement aij is multiplied by k…

Question

Match the following
Column-IColumn-II(i) Let |A| = |aij|3×3 ≠ 0. Eachelement aij is multiplied by kij.Let |B| the resultingDeterminant, where k1|A| +k2|B| = 0. Then k1 + k2 =[A] 0(ii) The maximum value of athird order determinant eachof its entries are ± 1 equals[B] 4(iii) if=thencos2α + cos2β + cos2γ =[C] 1(iv)= Ax + B where A and B aredeterminants of order 3.Then A + 2B =      [D] 2

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [A]; (ii) [B]; (iii) [C]; (iv) [A]. Ans.
(i) [A]
(ii) [B]
(iii) [C]
(iv) [A]
Sol. (i) |A| = 
|B| =    = |A|
k 1 |A| + k 2 |B| = 0
k 1 + k 2 = 0
(ii)  = 4
(iii) 
⇒ sin2 γ – cos α (cos α – cos β cos γ ) + cos β (cos α cos γ –cos β ) = – cos α (– cos β cos γ ) + cos β (cos α cos γ )
⇒ sin2 γ – cos2 α + 2cos α cos β cos γ – cos2 β
= 2 cos α cos β cos γ ⇒ sin2 γ = cos2 α + cos2 β ⇒ cos2 α + cos2 β + cos2 γ = 1
(iv) 
R 2 → R 2 – (R 1 + R 2 )
= 
=  = (24x – 12)
∴ A = 24, B = – 12
∴ A + 2B = 0

Text Solution

Prepare Smarter with CGP Edu

Write a Review

Commentary

Student Reviews

Similar Questions

Column-I	Column-II
(i) Let \|A\| = \|aij\|3×3 ≠ 0. Each element aij is multiplied by kij. Let \|B\| the resulting Determinant, where k1\|A\| + k2\|B\| = 0. Then k1 + k2 =	[A] 0
(ii) The maximum value of a third order determinant each of its entries are ± 1 equals	[B] 4
(iii) if= then cos2α + cos2β + cos2γ =	[C] 1
(iv) = Ax + B where A and B are determinants of order 3. Then A + 2B =	[D] 2

Share this question