Class 12 Math Algebra Determinants

If $A =⎣⎢⎡ 201 λ21 −353 ⎦⎥⎤ $ then $A_{−1}$ exists if

(a)

$λ=2$

(b)

$λ=2$

(c)

$λ=−2$

(d)

None of these

Correct answer: (d)

Solution: We have

$A =⎣⎢⎡ 201 λ21 −353 ⎦⎥⎤ $

expanding along $R_{1}$

$∣A∣=2(6−5)−λ(−5)−3(−2)=2+5λ+6$

we know that $A_{−1}$ exists , if $A$ is non-singular matrix i.e. $∣A∣=0$

$∴2+5λ+6=0$

$⇒5λ=neq−8$

$∴λ =5−8 $

So $A_{−1}$ exists if and only is $λ =5−8 $

$A =⎣⎢⎡ 201 λ21 −353 ⎦⎥⎤ $

expanding along $R_{1}$

$∣A∣=2(6−5)−λ(−5)−3(−2)=2+5λ+6$

we know that $A_{−1}$ exists , if $A$ is non-singular matrix i.e. $∣A∣=0$

$∴2+5λ+6=0$

$⇒5λ=neq−8$

$∴λ =5−8 $

So $A_{−1}$ exists if and only is $λ =5−8 $

Similar topics

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

determinants

matrices

binomial theorem

complex numbers and quadratic equations

sequences and series

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