The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
0 votes
277 views

What is R in this question? How to solve this?

Q).Let $A$ be a real $n*n$ matrix ,then which of the following statements are true?

I). $A$ is orthogonal iff the row vectors form an orthgonal set of vectors in $R^4$.

II). $A$ is orthogonal iff the columns vectors form an orthogonal set of vectors in $R^4$.

(A) Only I

(B) Only II

(C) Both I and II

(D) None of these

The correct answer is C. 

asked in Linear Algebra by Active (2.9k points)
retagged by | 277 views

1 Answer

+2 votes
Best answer

 Here R represents real number space and $4$ represents the dimensionality (number of coordinates to represent a point in space) of the real number space . Consider the following 2 diagrams 

                                   

Dimensions

Each vertex of a  cube is represented by $3$ coordinates $x,y,z$ . Since there are $3$ coordinates to represent each point on a cube so the cube is in three dimensional space. In case of this question there will be $4$ coordinates to represent a point 

Orthogonal Matrices:

Orthogonal matrices have two special properties 

  1. Each column has norm one, and each row has norm one.
  2. Each column is orthogonal to every other column, and each row is orthogonal to every other row

Since there are no numerical values for a matrix given so your answer is simply C

answered by Active (3.4k points)
selected by

Related questions

+1 vote
0 answers
2
asked Dec 12, 2017 in Linear Algebra by ankitgupta.1729 Boss (13.2k points) | 169 views
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,541 questions
54,084 answers
187,213 comments
70,992 users