in Linear Algebra retagged by
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Let P ≠ 0 be a 3 × 3 real matrix. There exist linearly independent vectors x and y such that
Px = 0 and Py = 0. The dimension of the range space of P is
[IE: GATE-2009]
 (a) 0 (b) 1 (c) 2 (d) 3
in Linear Algebra retagged by
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1 Answer

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I'm not sure whether I'm correct or not.

My approach is -

As Ax = 0 and Ay = 0 , so x and y are null space of A. So dimension of NullSpace = 2

now -

Dimension of Matrix(3) = Rank + Dimension of NullSpace(2)

so, Rank = 3 - 2 = 1

Now Range of a matrix means Column Space of Matrix.

So Dimension of Column Space of Matrix = Rank of Matrix = 1

So in my opinion 1 is the answer.

Please tell the correct answer.
edited by

4 Comments

Yes Dimension of Null Space means Nullity so yes understand it as Nullity
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@pilluverma123 @Prince Sindhiya

 Dimension of column space of a matrix is different from row space of matrix?

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