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Get Full Access to Linear Algebra Done Right (Undergraduate Texts In Mathematics) - 3 Edition - Chapter 5.c - Problem 16
Get Full Access to Linear Algebra Done Right (Undergraduate Texts In Mathematics) - 3 Edition - Chapter 5.c - Problem 16

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# The Fibonacci sequence F1; F2;::: is defined byF1 D 1; F2 D 1; and Fn D Fn2 C Fn1 for n ISBN: 9783319110790 432

## Solution for problem 16 Chapter 5.C

Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition

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Problem 16

The Fibonacci sequence F1; F2;::: is defined byF1 D 1; F2 D 1; and Fn D Fn2 C Fn1 for n 3:Define T 2 L.R2/ by T .x; y/ D .y; x C y/.(a) Show that T n.0; 1/ D .Fn; FnC1/ for each positive integer n.(b) Find the eigenvalues of T.(c) Find a basis of R2 consisting of eigenvectors of T.(d) Use the solution to part (c) to compute T n.0; 1/. Conclude thatFn D 1p51 C p52n1 p52n for each positive integer n.(e) Use part (d) to conclude that for each positive integer n, theFibonacci number Fn is the integer that is closest to1p51 C p52n

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1.5 Exponents and Radicals Math 1315-003 Shelley Hamilton Division with Exponents:  5^7/5^4 = 5^7-4 = 5^3  (-8) ^10/ (-8) ^5 = (-8) ^10-5 = (-8) ^5  (3c) ^9/(3c) ^3 = (3c) ^9-3 = (3c) ^6  (7*19) ^3 = (7*19) (7*19) (7*19) = 7*7*7*19*19*19 = 7^3 * 19^3 When dividing exponents, you just subtract the exponents as you can see in the examples above. Product to a power:  (ab)^n = a^n * b^n  Ex. (5y) ^3 = 5^3 y^3 = 125y^3  (c^2 d^3) ^4 = (c^2) ^4 (d^3) ^4  (x/2) ^6 = x^6/2^6 = x^6/64  (a^4/b^3) ^3 = a^12/b^9  When multiplying when there is an exponent in and one outside of the (). You multiply them together. Also, that exponent outside of the parenthesis, you distribute it in with the coefficient. Or every variable i

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##### ISBN: 9783319110790

This full solution covers the following key subjects: . This expansive textbook survival guide covers 31 chapters, and 560 solutions. The full step-by-step solution to problem: 16 from chapter: 5.C was answered by , our top Math solution expert on 03/15/18, 04:46PM. This textbook survival guide was created for the textbook: Linear Algebra Done Right (Undergraduate Texts in Mathematics), edition: 3. Linear Algebra Done Right (Undergraduate Texts in Mathematics) was written by and is associated to the ISBN: 9783319110790. The answer to “The Fibonacci sequence F1; F2;::: is defined byF1 D 1; F2 D 1; and Fn D Fn2 C Fn1 for n 3:Define T 2 L.R2/ by T .x; y/ D .y; x C y/.(a) Show that T n.0; 1/ D .Fn; FnC1/ for each positive integer n.(b) Find the eigenvalues of T.(c) Find a basis of R2 consisting of eigenvectors of T.(d) Use the solution to part (c) to compute T n.0; 1/. Conclude thatFn D 1p51 C p52n1 p52n for each positive integer n.(e) Use part (d) to conclude that for each positive integer n, theFibonacci number Fn is the integer that is closest to1p51 C p52n” is broken down into a number of easy to follow steps, and 108 words. Since the solution to 16 from 5.C chapter was answered, more than 213 students have viewed the full step-by-step answer.

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