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If A = [01312x231], A–1 = [12-452-123-3212y12] then x = 1, y = –1. - Mathematics

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प्रश्न

If A = `[(0, 1, 3),(1, 2, x),(2, 3, 1)]`, A–1 = `[(1/2, -4, 5/2),(-1/2, 3, -3/2),(1/2, y, 1/2)]` then x = 1, y = –1.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is True.

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अध्याय 4: Determinants - Solved Examples [पृष्ठ ७७]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 4 Determinants
Solved Examples | Q 18 | पृष्ठ ७७

संबंधित प्रश्न

Verify A (adj A) = (adj A) A = |A|I.

`[(1,-1,2),(3,0,-2),(1,0,3)]`


Find the inverse of the matrices (if it exists).

`[(1,2,3),(0,2,4),(0,0,5)]`


Find the adjoint of the following matrix:
\[\begin{bmatrix}- 3 & 5 \\ 2 & 4\end{bmatrix}\]

Verify that (adj A) A = |A| I = A (adj A) for the above matrix.

Find the adjoint of the following matrix:
\[\begin{bmatrix}a & b \\ c & d\end{bmatrix}\]

Verify that (adj A) A = |A| I = A (adj A) for the above matrix.

Find the adjoint of the following matrix:

\[\begin{bmatrix}1 & \tan \alpha/2 \\ - \tan \alpha/2 & 1\end{bmatrix}\]
Verify that (adj A) A = |A| I = A (adj A) for the above matrix.

Compute the adjoint of the following matrix:

\[\begin{bmatrix}2 & 0 & - 1 \\ 5 & 1 & 0 \\ 1 & 1 & 3\end{bmatrix}\]

Verify that (adj A) A = |A| I = A (adj A) for the above matrix.


For the matrix 

\[A = \begin{bmatrix}1 & - 1 & 1 \\ 2 & 3 & 0 \\ 18 & 2 & 10\end{bmatrix}\] , show that A (adj A) = O.

Find the inverse of the following matrix.

\[\begin{bmatrix}0 & 0 & - 1 \\ 3 & 4 & 5 \\ - 2 & - 4 & - 7\end{bmatrix}\]

For the following pair of matrix verify that \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1} :\]

\[A = \begin{bmatrix}3 & 2 \\ 7 & 5\end{bmatrix}\text{ and }B \begin{bmatrix}4 & 6 \\ 3 & 2\end{bmatrix}\]


For the following pair of matrix verify that \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1} :\]

\[A = \begin{bmatrix}2 & 1 \\ 5 & 3\end{bmatrix}\text{ and }B \begin{bmatrix}4 & 5 \\ 3 & 4\end{bmatrix}\]


Given  \[A = \begin{bmatrix}5 & 0 & 4 \\ 2 & 3 & 2 \\ 1 & 2 & 1\end{bmatrix}, B^{- 1} = \begin{bmatrix}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\] . Compute (AB)−1.


If \[A = \begin{bmatrix}3 & - 2 \\ 4 & - 2\end{bmatrix}\], find the value of \[\lambda\]  so that \[A^2 = \lambda A - 2I\]. Hence, find A−1.


If \[A = \begin{bmatrix}2 & - 1 & 1 \\ - 1 & 2 & - 1 \\ 1 & - 1 & 2\end{bmatrix}\].
Verify that \[A^3 - 6 A^2 + 9A - 4I = O\]  and hence find A−1.

If \[A = \frac{1}{9}\begin{bmatrix}- 8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & - 8 & 4\end{bmatrix}\],
prove that  \[A^{- 1} = A^3\]

If \[A = \begin{bmatrix}3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1\end{bmatrix}\] , show that \[A^{- 1} = A^3\]


If \[A = \begin{bmatrix}- 1 & 2 & 0 \\ - 1 & 1 & 1 \\ 0 & 1 & 0\end{bmatrix}\] , show that  \[A^2 = A^{- 1} .\]


Find the inverse by using elementary row transformations:

\[\begin{bmatrix}1 & 6 \\ - 3 & 5\end{bmatrix}\]


Find the inverse by using elementary row transformations:

\[\begin{bmatrix}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{bmatrix}\]


If \[A = \begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\] , then the value of |adj A| is _____________ .


For any 2 × 2 matrix, if \[A \left( adj A \right) = \begin{bmatrix}10 & 0 \\ 0 & 10\end{bmatrix}\] , then |A| is equal to ______ .


If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is _____________ .


If a matrix A is such that \[3A^3 + 2 A^2 + 5 A + I = 0,\text{ then }A^{- 1}\] equal to _______________ .


If \[A = \begin{bmatrix}2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2\end{bmatrix}\], find A−1 and hence solve the system of linear equations 2x − 3y + 5z = 11, 3x + 2y − 4z = −5, x + y + 2z = −3


Using matrix method, solve the following system of equations: 
x – 2y = 10, 2x + y + 3z = 8 and -2y + z = 7


If A and B are invertible matrices, then which of the following is not correct?


`("aA")^-1 = 1/"a"  "A"^-1`, where a is any real number and A is a square matrix.


|adj. A| = |A|2, where A is a square matrix of order two.


A and B are invertible matrices of the same order such that |(AB)-1| = 8, If |A| = 2, then |B| is ____________.


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