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 HKGC 高級會員 帖子685 積分815 註冊時間2010-9-12 [純數] linear combination 問題求高手入>,< #1 發表於 2017-10-6 08:06 AM  只看該作者 繁 簡 [按此打開] [隱藏] Screenshot (48).png (278.01 KB)question 322017-10-6 08:06 AM 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 .postmorevideochannel { margin-top: 10px; display: block; width: 160px; height: 30px; background: url('/images/video_channel_more.png?v=20160829b') no-repeat; font-size: 0; } .postmorevideochannel:hover, .postmorevideochannel:focus { background-position: 0 -30px; } @media (-webkit-min-device-pixel-ratio: 2), (min-resolution: 192dpi) { .postmorevideochannel { background: url('/images/video_channel_more_2x.png?v=20160829b') no-repeat; background-size: 100% auto; } }
 ppresent 一星級會員 帖子89 積分94 註冊時間2015-9-12 #2 發表於 2017-10-6 11:25 PM  只看該作者 繁 簡 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. [ 本帖最後由 ppresent 於 2017-10-7 10:35 AM 編輯 ] .postmorevideochannel { margin-top: 10px; display: block; width: 160px; height: 30px; background: url('/images/video_channel_more.png?v=20160829b') no-repeat; font-size: 0; } .postmorevideochannel:hover, .postmorevideochannel:focus { background-position: 0 -30px; } @media (-webkit-min-device-pixel-ratio: 2), (min-resolution: 192dpi) { .postmorevideochannel { background: url('/images/video_channel_more_2x.png?v=20160829b') no-repeat; background-size: 100% auto; } }

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