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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Chashokreddy18@gmail.com posted an Question
September 26, 2020 • 14:46 pm
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30 points
30 points
- CSIR NET
- Mathematical Sciences
Linear algebra - please explain the following problem(p:268). dimensions of subspaces of R^3(R)?
2 Answer(s)
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Deepak singh 1 Best Answer
clearly in W3 , x^2+y^2+z^2 = 0 iff x=y=z=0 so dim is 0 and in W4 for any value of x belongs to R , e^x always positive , so W4 is R3 and hence dimension of W4 is 3
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But the dimension of bit 3 is given as zero.
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how 0?
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here is the attachment.
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I have attached see in post ..
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feel free to ask again...
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Deepak singh 1![best-answer]()
see attached , it will clear your doubt..
Please explain.
Also I have seen problems where different formulae is used based on Q for finding the dimensions. I am really confused regarding applying correct formula to the given Q for finding dimensions. So, if possible could you please clarify regarding the formulae to be used for dimensions.
basis are same I.e (1,0,0) ,(0,1,0) and (0,0,1) because W4 is isomorphic to R^3.
try to do more questions based on finding dimensions.. then you will come to know more formulas and ideas..