मराठी

If a =`((5,A),(B,0))` Is Symmetric Matrix Show that a = B

Advertisements
Advertisements

प्रश्न

if A =`((5,a),(b,0))` is symmetric matrix show that a = b

Advertisements

उत्तर

A = `((5,a),(b,0))` given A is symmetric matrix

`A = A^T`

`[(5,a),(b,0)] = [(5,a),(b,0)]^T = [(5,b),(a,0)]`

`:. a = b`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2017-2018 (March) Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'


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

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


If the matrix A is both symmetric and skew symmetric, then ______.


Show that all the diagonal elements of a skew symmetric matrix are zero.


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


If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.


If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.


If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α


If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.


The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.


If A and B are matrices of same order, then (AB′ – BA′) is a ______.


Sum of two skew-symmetric matrices is always ______ matrix.


If A is symmetric matrix, then B′AB is ______.


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


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


Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.


What must be true of every diagonal element of a skew-symmetric matrix?


Which identity is used to replace \[(A^T)^T\] by \[A\] when proving that \[A+A^T\] is symmetric?


For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its symmetric part \[P=\frac{1}{2}(B+B^T)\]?


For the matrices \[P=\frac{1}{2}(B+B^T)\] and \[Q=\frac{1}{2}(B-B^T)\], what is \[P+Q\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×