Let A be a 3 - 3 matrix such that A- 1 2 3- 0 2 3- 0 1 1 - 0 0 1- 1 0 0- 0 1 0 -Then A-1 is -

The correct option is D [ 3 1 2; 3 0 2; 1 0 1 ] A×[ 1 amp; 2 amp; 3; 0 amp; 2 amp; 3; 0 amp; 1 amp; 1 ]=[ 0 amp; 0 amp; 1; 1 ...

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Standard XII

Mathematics

Adjoint of a Matrix

Let A be a ...

Question

Let A be a $3 \times 3$ matrix such that
$A \times ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 2 & 3 0 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$
Then $A^{- 1}$ is :

⎡ ⎢ ⎣ \begin{matrix} 3 & 2 & 1 3 & 2 & 0 1 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 3 0 & 2 & 3 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 1 0 & 2 & 3 \end{matrix} ⎤ ⎥ ⎦

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Solution

The correct option is D $⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$
$A \times ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 2 & 3 0 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$

$R o w R_{3} \leftrightarrow R_{1}, R_{2} \leftrightarrow R_{3}$

$A ⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = I$
$∴ A^{- 1} = ⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 2 3 & 0 & 2 1 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q. Let

A

and

B

3 \times 3

matrices such that

A^{T} = - A, B^{T} = B

, then matrix

(λ A B + 3 B A)

is a skew symmertric matrix for

Q. Let

A

be a

3 \times 3

matrix such that

a_{11} = a_{33} = 2

and all the other

a_{i j} = 1

. Let

A^{- 1} = x A^{2} + y A + z I

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(x + y + z)

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is a unit matrix of order

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, is-

Q. Let A be a matrix such that

A * [\begin{matrix} 1 & 2 0 & 3 \end{matrix}]

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| 3 A | = 108

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Q. Let

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being

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matrix and

x

is a real number such that

d e t (x A) = | x | . d e t (A)

, then

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Q. Let A be the matrix of order

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[Note : |A| represent determinant value of matrix A.]

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Let A be a 3×3 matrix such thatA×⎡⎢⎣123023011⎤⎥⎦=⎡⎢⎣001100010⎤⎥⎦Then A−1 is :

The correct option is D ⎡⎢⎣312302101⎤⎥⎦A×⎡⎢⎣123023011⎤⎥⎦=⎡⎢⎣001100010⎤⎥⎦RowR3↔R1,R2↔R3A⎡⎢⎣312302101⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I∴A−1=⎡⎢⎣312302101⎤⎥⎦

Let A be a $3 \times 3$ matrix such that
$A \times ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 2 & 3 0 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 1 1 & 0 & 0 0 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦$
Then $A^{- 1}$ is :