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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 (3.6k points)
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1 Answer

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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 



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 (3.5k points)
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