English

For the matrix A = [1567] verify that (A - A') is a skew symmetric matrix. - Mathematics

Advertisements
Advertisements

Question

For the matrix A = [1567] verify that (A - A') is a skew symmetric matrix.

Sum

Solution

Now, (A - A') = [1567]-[1657]

=[1-15-66-57-7]

=[0-110]

Then, (A - A') =[01-10]=- [0-110]

चूँकि (A - A') = -(A - A'),

Since (A - A') = -(A - A'), it proves that the matrix (A - A') is a skew symmetric matrix.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise 3.3 [Page 89]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 3 Matrices
Exercise 3.3 | Q 8.2 | Page 89

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Matrix A = [02b-23133a3-1]is given to be symmetric, find values of a and b


if A=[-123579-211]andB=[-41-5120131] then verify that (A- B)' = A' - B'


if A[34-1201]andB=[(-121123)] then verify that (A - B)' = A' - B'


For the matrices A and B, verify that (AB)′ = B'A' where A=[1-43],B=[-1,2 1]


If A = [cosαsinα-sinαcosα] then verify that  A' A = I


Show that the matrix  A = [01-1-1011-10] is a skew symmetric matrix.


For the matrix A = [1567] verify that (A + A') is a symmetric matrix.


Find 12 (A + A')  and  12 (A -A') When A=[0ab-a0c-b-c0]


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

[351-1]


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

[6-22-23-12-13]


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

[15-12]


If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix.


If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.


Write a square matrix which is both symmetric as well as skew-symmetric.


For what value of x, is the matrix  A=[012103x30]  a skew-symmetric matrix?


If A is a square matrix, then AA is a


If A and B are symmetric matrices, then ABA is


If A = [aij] is a square matrix of even order such that aij = i2 − j2, then 


If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is 


The matrix  A=[05850128120] is a 

 

Let A = [23-12]. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.


If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.


If A = [cosαsinα-sinαcosα], and A–1 = A′, find value of α


If A is a symmetric matrix, then A3 is a ______  matrix.


If A is a skew-symmetric matrix, then A2 is a ______.


If A and B are any two matrices of the same order, then (AB)′ = A′B′.


If A is skew-symmetric matrix, then A2 is a symmetric matrix.


If A and B are symmetric matrices of the same order, then ____________.


If A = [3x-12x+3x+2] is a symmetric matrix, then x = ____________.


If A is any square matrix, then which of the following is skew-symmetric?


If A, B are Symmetric matrices of same order, then AB – BA is a


The value of |A|, if A = [02x-1x1-2x02x-x-2x0], where x ∈ R+, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.