हिंदी

For the non singular matrix A, (A′)–1 = (A–1)′. - Mathematics

Advertisements
Advertisements

प्रश्न

For the non singular matrix A, (A′)–1 = (A–1)′.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Solved Examples [पृष्ठ ५२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 3 Matrices
Solved Examples | Q 18 | पृष्ठ ५२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


Find the value of a, b, c, and d from the equation:

`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`


Let A = `[(0,1),(0,0)]`show that (aI+bA)n  = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N


If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.


Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3


if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'


Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`


In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.


Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.


If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| . 


If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

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


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(5),(4),(-3)]`


Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`


Find k if the following matrix is singular:

`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`


Find k if the following matrix is singular:

`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`


If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.


Select the correct option from the given alternatives:

Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______


Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?


Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A


If A and B are matrices of same order, then (3A –2B)′ is equal to______.


If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2 


For any square matrix A, AAT is a ____________.


If a matrix A is both symmetric and skew-symmetric, then ____________.


If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.


If a matrix A is both symmetric and skew symmetric then matrix A is ____________.


`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?


If all the elements are zero, then matrix is said to be


A = `[a_(ij)]_(m xx n)` is a square matrix, if


If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to


Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0


A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.


Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.


If A is a square matrix of order 3, then |2A| is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×