मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: If A is a non singular matrix of order 3, then |adj (A)| = ______ - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

If A is a non singular matrix of order 3, then |adj (A)| =  ______

पर्याय

  • |A|2 

  • |A|3 

  • 0

  • 1

MCQ
रिकाम्या जागा भरा

उत्तर

|A|2 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.2: Matrices - Q.1

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.


Find the inverse of the following matrix (if they exist):

`[(3,-10),(2,-7)]`


Choose the correct answer from the given alternatives in the following question:

If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____


Find the inverse of the following matrices by transformation method:

`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`


If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.


Choose the correct alternative.

If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______


Choose the correct alternative.

If a 3 x 3 matrix B has it inverse equal to B, thenB2 = _______


Fill in the blank :

(AT)T = _______


State whether the following is True or False :

A(adj. A) = |A| I, where I is the unit matrix.


Check whether the following matrices are invertible or not:

`[(1, 0),(0, 1)]`


Find inverse of the following matrices (if they exist) by elementary transformations :

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


The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.


If ω is a complex cube root of unity, then the matrix A = `[(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)]` is


If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______


If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33.


For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.


A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1 


If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)


Find the adjoint of matrix A = `[(6, 5),(3, 4)]`


If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.


Find the inverse of the following matrix:

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


Find the inverse of the following matrix:

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


Solve by matrix inversion method:

2x + 3y – 5 = 0; x – 2y + 1 = 0.


If A = `((-1,2),(1,-4))` then A(adj A) is


If A and B non-singular matrix then, which of the following is incorrect?


Solve by using matrix inversion method:

x - y + z = 2, 2x - y = 0, 2y - z = 1


If A = `[(x,1),(1,0)]` and A = A , then x = ______.


If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______ 


If A2 - A + I = 0, then A-1 = ______.


If A = `[(5, -4), (7, -5)]`, then 3A-1 =  ______ 


If `A = [[-3,1],[-4,3]]` and A-1 = αA, then α = ______.


If A = `[(-i, 0),(0, i)]`, then ATA is equal to


If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =


Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.


If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I


If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`

Find (AB)–1 by adjoint method.

Solution:

AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`

AB = [  ]

|AB| =  `square`

M11 = –2  ∴ A11 = (–1)1+1 . (–2) = –2

M12 = –3     A12 = (–1)1+2 . (–3) = 3

M21 = 4       A21 = (–1)2+1 . (4) = –4

M22 = 3       A22 = (–1)2+2 . (3) = 3

Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`

adj (A) = [  ]

A–1 = `1/|A| . adj(A)`

A–1 = `square`


if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×