1. Let B = {v1,v2,...,vk} be a set of vectors in the space R5. The set of vectors B spans R5 if for every element v ∈ R5 there exist numbers α1,···αk ∈Rsuch that v = What is the minimal value of k for which this is possible? k =
can you solve the following problems?
1. Let B = {v1,v2,...,vk} be a set of vectors in the space R5.
The set of vectors B spans R5 if for every element v ∈ R5 there exist numbers
α1,···αk ∈Rsuch that
v =
What is the minimal value of k for which this is possible?
k =
2. Let B = {v1,v2,...,vk} be a set of vectors in the space R4.
a) Complete the following definitions
Def. 1. The set of vectors B spans R4 if for every element u ∈ R5 there exist numbers
α1,···αk∈Rsuch that
u =
What is the minimal value of k for which this is possible?
k =
Does the following vectors span R4 -Why or Why not??-Explain.
a1 = <3, cos 10, sin 11, 1>
a2= <0, tan 13, sin 50, 2>
a3= < √2, 0√23, −√7>
3. the matrix A= 1 0 1 1 2
0 0 1 1 1
0 0 0 1 1
d) Find a basis B1 of ColA consisting entirely of columns of A.
(e) Find a second basis B2 of ColA consisting entirely of columns of A, or explain why such a
basis does not exist.
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