when two sets of vectors have the same all linear combinations?











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I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T



S={v1,v2,v3,v4} this one is dependent
T={v1,v2,v4} this one is independent
as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?






linear-algebra







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    up vote
    0
    down vote

    favorite












    I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T



    S={v1,v2,v3,v4} this one is dependent
    T={v1,v2,v4} this one is independent
    as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?






    linear-algebra







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T



      S={v1,v2,v3,v4} this one is dependent
      T={v1,v2,v4} this one is independent
      as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?






      linear-algebra







      share|cite|improve this question













      I don't know how to solve this kind of question this is my issue firstly I'm given tow sets of vectors S,T



      S={v1,v2,v3,v4} this one is dependent
      T={v1,v2,v4} this one is independent
      as you may notice the set T is a subset of S which has the same vectors except {v3} then how to show that the two sets have the same all linear combinations?






      linear-algebra




      linear-algebra






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 8 hours ago









      faisal

      51




      51






















          1 Answer
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          accepted










          We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.



          Hence adding $v_3$ doesn't change the span.






          share|cite|improve this answer





















          • sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
            – faisal
            7 hours ago










          • If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
            – Siong Thye Goh
            6 hours ago










          • thank you, sir, you are really great
            – faisal
            6 hours ago











          Your Answer





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          1 Answer
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          active

          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote



          accepted










          We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.



          Hence adding $v_3$ doesn't change the span.






          share|cite|improve this answer





















          • sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
            – faisal
            7 hours ago










          • If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
            – Siong Thye Goh
            6 hours ago










          • thank you, sir, you are really great
            – faisal
            6 hours ago















          up vote
          0
          down vote



          accepted










          We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.



          Hence adding $v_3$ doesn't change the span.






          share|cite|improve this answer





















          • sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
            – faisal
            7 hours ago










          • If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
            – Siong Thye Goh
            6 hours ago










          • thank you, sir, you are really great
            – faisal
            6 hours ago













          up vote
          0
          down vote



          accepted







          up vote
          0
          down vote



          accepted






          We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.



          Hence adding $v_3$ doesn't change the span.






          share|cite|improve this answer












          We just have to show that $v_3$ can be expressed as a linear combination of $v_1, v_2, v_4$.



          Hence adding $v_3$ doesn't change the span.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 8 hours ago









          Siong Thye Goh

          92.9k1462114




          92.9k1462114












          • sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
            – faisal
            7 hours ago










          • If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
            – Siong Thye Goh
            6 hours ago










          • thank you, sir, you are really great
            – faisal
            6 hours ago


















          • sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
            – faisal
            7 hours ago










          • If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
            – Siong Thye Goh
            6 hours ago










          • thank you, sir, you are really great
            – faisal
            6 hours ago
















          sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
          – faisal
          7 hours ago




          sorry, sir could you please explain what does it mean when two sets of vectors have the same all linear combinations?
          – faisal
          7 hours ago












          If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
          – Siong Thye Goh
          6 hours ago




          If we let $A = span{ v_1, v_2, v_3, v_4}$ and $B = span{ v_1, v_2, v_4}$. Then the two sets $A$ and $B$ are the same.
          – Siong Thye Goh
          6 hours ago












          thank you, sir, you are really great
          – faisal
          6 hours ago




          thank you, sir, you are really great
          – faisal
          6 hours ago


















           

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