Let A be a 3 - 3 matrix such that - P- begin b m a t r i x 18 alpha- 3 1 18383112 - 4 - 4lend bmatrix - P -adj A and - A -4-thenthevalueof - isA- 11B- 12C- 20D- 15

The correct option is A 11Given, P=adj(A) ⇒ |P|=|adj(A)| ⇒ |P|=|A|^3 1=|A|^2 ⇒ 1 amp;α amp;3 1 amp;3 amp;3 2 amp;4 amp;4 =16 ⇒1(12 12) α(4 6)+3( ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Determinants

Let A be a 3 ...

Question

Let $A$ be a $3 \times 3$ matrix such that $P = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦,$ $P = a d j (A)$ and $| A | = 4,$ then the value of $α$ is

11

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

15

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $11$
Given, $P = a d j (A)$
$\Rightarrow | P | = | a d j (A) |$
$\Rightarrow | P | = | A |^{3 - 1} = | A |^{2}$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ∣ ∣ ∣ ∣ = 16$

$\Rightarrow 1 (12 - 12) - α (4 - 6) + 3 (4 - 6) = 16 \Rightarrow 2 α - 6 = 16 ∴ α = 11$

Suggest Corrections

Similar questions

Q. Let

A

be a

3 \times 3

matrix such that

P = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦,

P = a d j (A)

and

| A | = 4,

then the value of

α

Q. If matrix

P = ∣ ∣ ∣ ∣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ∣ ∣ ∣ ∣

is the adjoint of a

3 \times 3

matrix A and |A| = 4, then

α

is equal to

Q. Let

P = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦

and

I

be the identity matrix of order

3

. If

Q = [q_{i j}]

is a matrix, such that

p^{50} - Q = I

, then

\frac{q_{31} + q_{32}}{q_{21}}

equals

Q. If

P = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦

is the adjoint of a

3 \times 3

matrix

A

and

| A | = 4

, then

α

is equal to:

Q. If

P = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦

is the adjoint of a

3 \times 3

matrix

A

and

| A | = 4

, then

α

is equal to

Join BYJU'S Learning Program

Let A be a 3×3 matrix such that P=⎡⎢⎣1α3133244⎤⎥⎦, P=adj(A) and |A|=4, then the value of α is

The correct option is A 11Given, P=adj(A) ⇒|P|=|adj(A)| ⇒|P|=|A|3−1=|A|2 ⇒∣∣ ∣∣1α3133244∣∣ ∣∣=16 ⇒1(12−12)−α(4−6)+3(4−6)=16⇒2α−6=16∴α=11

Let $A$ be a $3 \times 3$ matrix such that $P = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦,$ $P = a d j (A)$ and $| A | = 4,$ then the value of $α$ is