(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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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