Show that A' A and A A' are both symmetr...

Show that A' A and A A' are both symmetric matrices for any matrix A.

Text Solution

AI Generated Solution

To show that \( A^T A \) and \( A A^T \) are both symmetric matrices for any matrix \( A \), we will follow these steps: ### Step 1: Show that \( A^T A \) is symmetric 1. **Define the matrix**: Let \( P = A^T A \). 2. **Find the transpose of \( P \)**: \[ P^T = (A^T A)^T ...

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

LINEAR PROGRAMMING
NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|2 Videos
PROBABILITY
NCERT EXEMPLAR ENGLISH|Exercise True/False|9 Videos

Similar Questions

Explore conceptually related problems

A A' is always a symmetric matrix for any matrix A.

If A and B are symmetric matrices, then ABA is

If A is any mxxn such that A B and B A are both defined show that B is an nxxm matrix.

Let a be square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.

Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) and (AB)A are symmetric matrices. Statement 2 : AB is symmetric matrix if matrix multiplication of A with B is commutative.

If A and B are symmetric matrices, then A B A is (a) symmetric matrix (b) skew-symmetric matrix (c) diagonal matrix (d) scalar matrix

If [(3,5),(7,9)] is written as A + B, where A is the skew-symmetric matrix and B is the symmetric matrix, then write the matrix A.

If A and B are symmetric matrices of order n(A!=B) then (A) A+B is skew symmetric (B) A+B is symmetric (C) A+B is a diagonal matrix (D) A+B is a zero matrix

Choose the correct answer If A, B are symmetric matrices of same order, then AB – BA is a (A) Skew symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix

If A and B are symmetric matrices of the same order, show that AB+BA is symmetric.

NCERT EXEMPLAR ENGLISH-MATRICES-Solved example

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify...
03:42
|
If A=[{:(1,2),(4,1),(5,6):}] and B=[{:(1,2),(6,4),(7,3):}], then varif...
03:20
|
Show that A' A and A A' are both symmetric matrices for any matrix A.
02:06
|
Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...
01:19
|
Show that , if A and B are square matrices such that AB=BA, then (A+B)...
01:37
|
If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}] a=4 an...
02:57
|
If A=[{:(cos q,sin q),(-sin q, cos q):}] , then variefy that A^(2)=[{:...
04:41
|
If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show ...
02:36
|
Verify that A^(2)=I, when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]
04:10
|
If A is a square matrix, using mathematical induction prove that (A...
03:10
|
Find inverse, by elementary row operations (if possible) , of both fo...
04:15
|
If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}], then find the values of x...
02:52
|
If A=[{:(1,5),(7,12):}] and B=[{:(9,1),( 7,8):}] then find a matrix C ...
04:07
|
If A=[{:(3,-5),(-1,2):}] then find A^(2)-5A- 4I.
04:22
|
Find the values of a,b,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,2...
03:02
|
Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10)...
04:22
|
If A=[{:(1,2),(4,1):}] , then find A^(2)+2A+7I.
04:24
|
If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A'...
01:56
|
If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, the...
01:22
|
If P(x)=[(cosx, sinx),(-sinx, cosx)], then show that P(x).P(y)=P(x+y)=...
06:16
|