हिंदी

If A is a square matrix of order 3, |A′| = −3, then |AA′| = ______. - Mathematics

Advertisements
Advertisements

प्रश्न

If A is a square matrix of order 3, |A′| = −3, then |AA′| = ______.

विकल्प

  • 9

  • −9

  • 3

  • −3

MCQ
रिक्त स्थान भरें

उत्तर

If A is a square matrix of order 3, |A′| = −3, then |AA′| = 9.

Explanation:

|AA'| = |A||A'|

= (−3)(−3)

= 9

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2022-2023 (March) Sample

संबंधित प्रश्न

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

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


If A = `[(3,1),(-1,2)]` show that A2 – 5A + 7I = O. Hence, find A–1.


For the matrix A = `[(1,1,1),(1,2,-3),(2,-1,3)]` show that A3 − 6A2 + 5A + 11 I = O. Hence, find A−1.


If A is an invertible matrix of order 2, then det (A−1) is equal to ______.


If `A^(-1) =[(3,-1,1),(-15,6,-5),(5,-2,2)]` and `B = [(1,2,-2),(-1,3,0),(0,-2,1)]`  find  `(AB)^(-1)`


Find the inverse of the following matrix:

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

Find the inverse of the following matrix.

\[\begin{bmatrix}1 & 0 & 0 \\ 0 & \cos \alpha & \sin \alpha \\ 0 & \sin \alpha & - \cos \alpha\end{bmatrix}\]

Find the inverse of the following matrix and verify that \[A^{- 1} A = I_3\]

\[\begin{bmatrix}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\]

Let \[A = \begin{bmatrix}3 & 2 \\ 7 & 5\end{bmatrix}\text{ and }B = \begin{bmatrix}6 & 7 \\ 8 & 9\end{bmatrix} .\text{ Find }\left( AB \right)^{- 1}\]


Given \[A = \begin{bmatrix}2 & - 3 \\ - 4 & 7\end{bmatrix}\], compute A−1 and show that \[2 A^{- 1} = 9I - A .\]


Let
\[F \left( \alpha \right) = \begin{bmatrix}\cos \alpha & - \sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{bmatrix}\text{ and }G\left( \beta \right) = \begin{bmatrix}\cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ - \sin \beta & 0 & \cos \beta\end{bmatrix}\]

Show that

(i) \[\left[ F \left( \alpha \right) \right]^{- 1} = F \left( - \alpha \right)\]
(ii) \[\left[ G \left( \beta \right) \right]^{- 1} = G \left( - \beta \right)\]
(iii) \[\left[ F \left( \alpha \right)G \left( \beta \right) \right]^{- 1} = G \left( - \beta \right)F \left( - \alpha \right)\]

Find the inverse by using elementary row transformations:

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


Find the inverse by using elementary row transformations:

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


Find the inverse by using elementary row transformations:

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


Find the inverse by using elementary row transformations:

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


If A, B are two n × n non-singular matrices, then __________ .


If \[A = \begin{bmatrix}1 & 2 & - 1 \\ - 1 & 1 & 2 \\ 2 & - 1 & 1\end{bmatrix}\] , then ded (adj (adj A)) is __________ .


The matrix \[\begin{bmatrix}5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b\end{bmatrix}\] is a singular matrix, if the value of b is _____________ .


If \[A^2 - A + I = 0\], then the inverse of A is __________ .


If \[A = \begin{bmatrix}2 & - 1 \\ 3 & - 2\end{bmatrix},\text{ then } A^n =\] ______________ .

Find A−1, if \[A = \begin{bmatrix}1 & 2 & 5 \\ 1 & - 1 & - 1 \\ 2 & 3 & - 1\end{bmatrix}\] . Hence solve the following system of linear equations:x + 2y + 5z = 10, x − y − z = −2, 2x + 3y − z = −11


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


|A–1| ≠ |A|–1, where A is non-singular matrix.


If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of `1/(1+"a") + 1/(1+"b") + 1/(1+"c")` is ____________.


For matrix A = `[(2,5),(-11,7)]` (adj A)' is equal to:


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


If for a square matrix A, A2 – A + I = 0, then A–1 equals ______.


To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their residential colony, where they sold paper bags, scrap books and pastel sheets made by using recycled paper. Student of school A sold 30 paper bags, 20 scrap books and 10 pastel sheets and raised ₹ 410. Student of school B sold 20 paper bags, 10 scrap books and 20 pastel sheets and raised ₹ 290. Student of school C sold 20 paper bags, 20 scrap books and 20 pastel sheets and raised ₹ 440.

Answer the following question:

  1. Translate the problem into a system of equations.
  2. Solve the system of equation by using matrix method.
  3. Hence, find the cost of one paper bag, one scrap book and one pastel sheet.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×