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nin

  • 3 years ago

Is this set a basis to R3? [1] [3] [0] [2] [2] [0] [3] [1] [1] What method is used? Thank You

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  1. mathTalk
    • 3 years ago
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    For vectors to belong to the set of basis 1. they should be linearly independent 2. They should span the space R3.

  2. nin
    • 3 years ago
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    Okay, would proving the determinant is non-zero be sufficient?

  3. mathTalk
    • 3 years ago
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    That would probably prove that they are linearly independent right? you will have to show that for any point (a,b,c) in R3 (a,b,c) = k1v1+k2v2+k3v3

  4. mathTalk
    • 3 years ago
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    in addition.

  5. nin
    • 3 years ago
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    Yes i see. Linear independence would be proved. After making Linear combinations would i then sub in a=0, b=0 and c=0 to see if k1=k2=k3=0?

  6. mathTalk
    • 3 years ago
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    yess.

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