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HKGC 2017-10-6 08:06 AM

linear combination 問題求高手入>,<

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想問QUESTION 32 點解係UNFINITE SOLUTION 同埋係咪所有係個PLANE 入面GA VECTOR 都係SOLUTION?
另外, 如果係無解/唯一 的時候幅圖又係點? THANK YOU

ppresent 2017-10-6 11:25 PM

Because these vectors v1,v2,v3 are in R2 and you can see that they are pointing at different directions, so there are 2 independent vectors in them and they span the whole vector space R2. Any vector in R2(including b) can be written as linear combinations of v1 & v2 and at least one solution can be found for it. There is an extra column here and associates with it a free variable so there would be infinite solutions.

In the case of no solution you may think of v1,v2,v3 all pointing to the same direction and that b is in another direction. This equation wouldn't have a case of one solution because as mentioned you have an extra column and a free variable.

[[i] 本帖最後由 ppresent 於 2017-10-7 10:35 AM 編輯 [/i]]
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