Question 15. (a) Let {v1, . . . , vn} be a spanning set for the vector space V , and let v be any other vector in V . Show that v, v1, . . . , vn are linearly dependent.
(b) Let v1,v2,...,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot spanV.

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22-06-2024
Mathematics

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Question 15. (a) Let {v1, . . . , vn} be a spanning set for the vector space V , and let v be any other vector in V . Show that v, v1, . . . , vn are linearly dependent.
(b) Let v1,v2,...,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot spanV.

Sagot :

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Question 15. (a) Let {v1, . . . , vn} be a spanning set for the vector space V , and let v be any other vector in V . Show that v, v1, . . . , vn are linearly dependent. (b) Let v1,v2,...,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot spanV.

Sagot :

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Question 15. (a) Let {v1, . . . , vn} be a spanning set for the vector space V , and let v be any other vector in V . Show that v, v1, . . . , vn are linearly dependent.
(b) Let v1,v2,...,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot spanV.