In Example 3 we showed that an appropriate choice of basis could greatly simplify the computation of
Question:
1. Let
And
(a) Show that S is a basis for R2.
(b) Find [v] S.
(c) Determine a scalar (1 such that Av1, = (1v1.
(d) Determine a scalar (2 such that Av2 = (2v2.
(e) Use the basis S and the results of parts (b) through (d) to determine an expression for Anv that is a linear combination of v1 and v2.
(f) As n increases, describe the limiting behavior of the sequence Av, A2v, A3v, ( ( ( ( Anv, ( ( ( (
2. Let
And
Follow the directions for (a) through (f) in Exercise 13.
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
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