- #1
flyingpig
- 2,579
- 1
Homework Statement
http://img6.imageshack.us/img6/5017/69430037.th.png
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The Attempt at a Solution
a) [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP10519f5ffahf530d2ei00005867aii1c038ibgc?MSPStoreType=image/gif&s=29&w=178&h=56
[PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP10819f5ffahf530d2ei0000437856bcgaif2657?MSPStoreType=image/gif&s=29&w=73&h=56
So the vectors that form the basis are <1,-2,7> and <4,1,4>
The dimension of the subspace is 2 right? Because the two vectors <1,-2,7> and <4,1,4> form a plane in R3? Is it a coincidence that this is the same as finding a basis for the column space?
b) [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP125919f5fc52791ag4c6000014fi7d54aa6g5d94?MSPStoreType=image/gif&s=31&w=167&h=56
[PLAIN]http://www4b.wolframalpha.com/Calculate/MSP/MSP299519f5f8h0d007afe50000540gfh59c2d627f5?MSPStoreType=image/gif&s=40&w=62&h=56
So there is a pivot in every row/column, then <1,1,1> is indeed in W
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