If A=α 22 α and A3=27 , then the value of α is:

Given: A=α 22 αSince, det⁡An=(det⁡(A))n⇒A3=|A|3So,|A|3=A3⇒α2−43=27⇒α2−4=3⇒α=±7

If A=α 22 α and A3=27 , then the value of α is:

Given: A=α 22 αSince, det⁡An=(det⁡(A))n⇒A3=|A|3So,|A|3=A3⇒α2−43=27⇒α2−4=3⇒α=±7

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $A = [\begin{array}{ll} α 2 \\ 2 α \end{array}] and |A^{3}| = 27$ , then the value of α is:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

±√7

±1

±2

±√5

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given: $A = [\begin{array}{ll} α 2 \\ 2 α \end{array}]$
Since, $\det (A^{n}) = (\det (A))^{n}$
$\begin{array}{l} \Rightarrow |A^{3}| = | A |^{3} \\ S o, | A |^{3} = |A^{3}| \\ \Rightarrow {(α^{2} - 4)}^{3} = 27 \\ \Rightarrow α^{2} - 4 = 3 \\ \Rightarrow α = \pm \sqrt{7} \end{array}$