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In Exercises $27-30$ , use coordinate vectors to test the linear independence of the sets of polynomials. Explain your work.$$(2-t)^{3},(3-t)^{2}, 1+6 t-5 t^{2}+t^{3}$$

$(2-t)^{3},(3-t)^{2}, 1+6 t-5 t^{2}+t^{3}$ are not linearly independent.

Calculus 3

Chapter 4

Vector Spaces

Section 4

Coordinate Systems

Vectors

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In mathematics, a vector (…

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In Exercises $27-30$ , use…

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In Exercises 33 and $34,$ …

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In Exercises $15-22,$ use …

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In Exercises $17-20,$ show…

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Show that the given vector…

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Show that the three soluti…

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In Exercises 33 and $34, T…

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In Exercises 21- 30, descr…

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in this problem we're given a Senate. Were test those for linear get fancy. Let's first right. Let's first explain these pollutants or this is R P one p to a This is B B C P. One is eight minus 12 T plus 60 spread minus you. And if you were to write the basis so I write the important factor for people in that would be age negative 12 6 and 91. So the first time is basically the corruption, but he's your firm t one t 2 23 So dumpy to would be an expanded on written is nine minus 60 plus t squared. So they recorded. Lecture her pee, too. It would be nine negative 61 and zero and P three is already an expanded form. So one plus 60 minus five piece fried. Let's take you so it only Cordant back through four p three with little A, um 16 and 8 to 5 for one. So let's write. Be augmented Major's phone like these porn in vectors. We have a JJ negative 12 6 negative one mine. 96 10 in 16 negative five and one a CZ you can see from here. Okay, First, let's rename those lectures us, B, B one, B two and B. As you can see, we can write be three as a combination of the term you want. So what does B B three's even privy to minus We want, since we can write one of the factors as a combination of others were going to say, That piece hold on the over this system is linearly depended.

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