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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Yash Singh posted an Question
January 16, 2020 • 03:29 am
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15 points
15 points
- IIT JAM
- Mathematics (MA)
71. Consider the following subspace of R°: W={r, y,z)ER' :2x+2y+z 0,3x+3y-2z = 0, x+y-3z = 0 The dimension of Wis (a) 0 b) 1 (d) 3 (c) 2
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Priyadarshan Choursiya Best Answer
here I will give you a short cut that. in such type of questions, the dimension is reduce by the given no. of conditions provided the conditions are linear independent. i.e dim(R^n) =n. W is subspace of Rn with k Linear independent conditions then dim(W)= n-k. here you see that second condition is linear combination of first and third. so actually there are only two linear independent conditions. therefore dimensions of W =3-2=1. I think you also know that the number of unknown is the dimension for Rn, there subspaces, and of metrics if you don't got my point please see last part of attachment. complete proof in the attachment-
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Priyadarshan Choursiya
what kind of clearfication you want. I don't got that, I give you complete solution. what is your question I don't follow. can you clear it