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(3) §4.4, Suppose b1, , bn in a vector space V are linearly independent. Suppose span{b1, , bn} ... .... #V. Show that there is v E V such that {b1, , bn,v} is linearly independent. (4) §4.4, Suppose b1,, b, in a vector space V over F are linearly independent. Let B=span{b1, ... ,bn}. Then we know each vector b E B can be written as b = cb1 + ... c2b2 + · · · + Cnbn for some ck E F. Show that c1, C2,, Cn are unique.

(3) §4.4, Suppose b1, , bn in a vector space V are linearly independent. Suppose span{b1, , bn} ... .... #V. Show that there is v E V such that {b1, , bn,v} is linearly independent. (4) §4.4, Suppose b1,, b, in a vector space V over F are linearly independent. Let B=span{b1, ... ,bn}. Then we know each vector b E B can be written as b = cb1 + ... c2b2 + · · · + Cnbn for some ck E F. Show that c1, C2,, Cn are unique.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) §4.4, Suppose b1, · · · , bn in a vector space V are linearly independent. Suppose span{b1, , b,} #V. Show that there is v E V such that {b1, , bn, v} is linearly independent. (4) §4.4, Suppose b1,, bn in a vector space V over F are linearly independent. Let B=span{b1, , bn}. Then we know each vector b EB can be written as b = cb + c2b2 + ...+ Cnbn for some c E F. Show that c1, c2,·, Cn are unique.
Transcribed Image Text:(3) §4.4, Suppose b1, · · · , bn in a vector space V are linearly independent. Suppose span{b1, , b,} #V. Show that there is v E V such that {b1, , bn, v} is linearly independent. (4) §4.4, Suppose b1,, bn in a vector space V over F are linearly independent. Let B=span{b1, , bn}. Then we know each vector b EB can be written as b = cb + c2b2 + ...+ Cnbn for some c E F. Show that c1, c2,·, Cn are unique.
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