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Show that the signals in Exercises $3-6$ form a basis for the solution set of the accompanying difference equation. The signals and equation in Exercise 1

the given signals $\left\{ 2 ^ { k } , ( - 4 ) ^ { k } \right\}$ are linearly independent.

Calculus 3

Chapter 4

Vector Spaces

Section 8

Applications to Difference Equations

Vectors

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wick of these two signals from problems 03 to decay in minor street like a. And we need to see you too, so that the V's two signals form a basis for the solution set off the other line. This could be gruesome. We will apply like a sorority test, which you can find it at the end off things to four. Seven from the book. And we consider the casserole schematics off the system, which is this one. And the girls are the best. Says that if these Matics isn't very people for at least one K then without Hlynur its independence. Um, so we try for simplicity toe study The turbulent off these mavericks four k equals zero. That is the definite off the mavericks one city well minus three on these evaluates not my arms. Three mind must say with equals minus six, which is other than zero. So this mattress is in vegetable and we have lena have independence off the solution. Um, this fucking it's consistent with theory 17 from Bates 2 50 that says that this solution off the often and for their described the Anamika discreet occasion forms sodium Asian funds to two dimensional solutions

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