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Write the difference equations in Exercises 29 and 30 as first-order systems, $\mathbf{x}_{k+1}=A \mathbf{x}_{k},$ for all $k$ $$y_{k+3}-\frac{3}{4} y_{k+2}+\frac{1}{16} y_{k}=0$$

$x _ { k + 1 } = A x _ { k }$

Calculus 3

Chapter 4

Vector Spaces

Section 8

Applications to Difference Equations

Vectors

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we will right this third or their difference occasion as the first or the system in the form X killed plus one. We will write it with over line just to know that this is a vector. It was a times ex gay Which way is three is three times three mavericks Since we'll have the thunder, their system and we proceed by considering the vector x t Uh, it's consistent these three values and the vector x k plus one which is this vector for following the definition off ex gay and we write Get with the foot taking the talk on the information from thing this and get some of them got played Tow the federal court in areas see off Gabe Plus three equals three over four CK plus two minus one over 16 ck and we perceive as in the book. And, uh, that's an example of the book. And we write it as they seduce them in the for month eight times ck where a equals one or one 01 and minus one over. So extreme. Oh, and city over four. All of these times, the vector X Games

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