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Linear Independence and Spanning

  • Thread starter Jack Nagel
  • Start date
  • #1
Say that {W1, W2, W3, W4} is linearly independent in R4.

Now say I have this vector
[ 2
tan(h)
7
4sec(k)
]

and I want to find values of h and k such that it is not in the span of (W1...W4).

If I understand this correctly, it means it is impossible to find those values since they do not exist. If a set of 4 vectors in R4 are linearly independent, then they also span R4.

Am I right or way off on this?
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
18
That sounds right.
 

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