Let A=[ -4 -3 -3 1 a 1 4 b 3 ] and A=A- 1 , then a+2b is equal to

Question

Let A=[ -4 -3 -3 1 a 1 4 b 3 ] and A=A- 1 , then a+2b is equal to (A) 0 (B) 4 (C) 8 (D) 5

Tardigrade Admin · Accepted Answer

∴ A=A- 1⇒ A2=I A2 = A ⋅ A = [ - 4 - 3 - 3 1 a 1 4 b 3 ] [ - 4 - 3 - 3 1 a 1 4 b 3 ] =[ 1 12-3a-3b 0 a -3+a2+b a b-4 -12+ab+3b b-3 ] ∴ A2=I⇒ a=0,b=4⇒ a+2b=8

Q. Let $A = ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤$ and $A = A^{- 1}$ , then $a + 2 b$ is equal to

$0$

$4$

$8$

$5$

$∴ A = A^{- 1} \Rightarrow A^{2} = I$
$A^{2} = A \cdot A = ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤ ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤$
$= ⎣ ⎡ 1 a b - 4 12 - 3 a - 3 b - 3 + a^{2} + b - 12 + ab + 3 b 0 a b - 3 ⎦ ⎤$
$∴ A^{2} = I \Rightarrow a = 0, b = 4 \Rightarrow a + 2 b = 8$

Q. Let A=⎣⎡​−414​−3ab​−313​⎦⎤​ and A=A−1 , then a+2b is equal to

0

4

8

5

∴A=A−1⇒A2=I A2=A⋅A=⎣⎡​−414​−3ab​−313​⎦⎤​⎣⎡​−414​−3ab​−313​⎦⎤​ =⎣⎡​1ab−4​12−3a−3b−3+a2+b−12+ab+3b​0ab−3​⎦⎤​ ∴A2=I⇒a=0,b=4⇒a+2b=8

Q. Let $A = ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤$ and $A = A^{- 1}$ , then $a + 2 b$ is equal to

$0$

$4$

$8$

$5$

$∴ A = A^{- 1} \Rightarrow A^{2} = I$
$A^{2} = A \cdot A = ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤ ⎣ ⎡ - 4 14 - 3 a b - 3 13 ⎦ ⎤$
$= ⎣ ⎡ 1 a b - 4 12 - 3 a - 3 b - 3 + a^{2} + b - 12 + ab + 3 b 0 a b - 3 ⎦ ⎤$
$∴ A^{2} = I \Rightarrow a = 0, b = 4 \Rightarrow a + 2 b = 8$