If A = 1 - 2 1 2 λ - 2 1 3 - 3 be the adjoint matrix of matrix B such that B = 9 , then the value of λ is equal to

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If

A = [\begin{array}{l} 1 & - 2 & 1 \\ 2 & λ & - 2 \\ 1 & 3 & - 3 \end{array}]

be the adjoint matrix of matrix

B

such that

|B| = 9

, then the value of

λ

is equal to

MathematicsDeterminantsJEE Main

Options:

A $1$
B $\frac{- 77}{4}$
C $\frac{23}{2}$
D $\frac{- 39}{2}$

Solution:

2452 Upvotes Verified Answer

The correct answer is:

\frac{- 77}{4}

A = a d j (B)

|A| = {|B|}^{2}

|\begin{array}{l} 1 & - 2 & 1 \\ 2 & λ & - 2 \\ 1 & 3 & - 3 \end{array}| = 81

\Rightarrow 1 (- 3 λ + 6) + 2 (- 6 + 2) + 1 (6 - λ) = 81

\Rightarrow - 4 λ + 4 = 81

\Rightarrow λ = - \frac{77}{4}

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play