If P- 1 - 3- 1 3 3- 2 4 4 - is the adjoint of a 3- 3 matrix A and -A-4- then - is equal to -

Adj (A)=[ 1 amp;α amp;3; 1 amp;3 amp;3; 2 amp;4 amp;4 ] As we know, |adj(A)|=|A|^2 ⇒ 1(12 12) α(4 6)+3(4 6)=(4)^2 ⇒α=11 ...

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Byju's Answer

Standard XIII

Mathematics

Adjoint of a Matrix

If P=[ 1 α 3;...

Question

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 :

4

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11

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Solution

The correct option is B $11$
$adj (A) = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦$
As we know,
$| adj (A) | = | A |^{2}$
$\Rightarrow 1 (12 - 12) - α (4 - 6) + 3 (4 - 6) = (4)^{2}$
$\Rightarrow α = 11$

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Similar questions

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 & c & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦

is the adjoint of a

3 \times 3

matrix

Q

and

det Q = 4

, then the value of

c

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 :

Q. If

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

is the adjoint of

3 \times 3

matrix

A

and

| A | = 4

, then

α

is equal to

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If P=⎡⎢⎣1α3133244⎤⎥⎦ is the adjoint of a 3×3 matrix A and |A|=4, then α is equal to :

The correct option is B 11adj(A)=⎡⎢⎣1α3133244⎤⎥⎦ As we know, |adj(A)|=|A|2 ⇒1(12−12)−α(4−6)+3(4−6)=(4)2 ⇒α=11

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 :

The correct option is B $11$
$adj (A) = ⎡ ⎢ ⎣ \begin{matrix} 1 & α & 3 1 & 3 & 3 2 & 4 & 4 \end{matrix} ⎤ ⎥ ⎦$
As we know,
$| adj (A) | = | A |^{2}$
$\Rightarrow 1 (12 - 12) - α (4 - 6) + 3 (4 - 6) = (4)^{2}$
$\Rightarrow α = 11$