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Consider the polynomials $\mathbf{p}_{1}(t)=1+t^{2}$ and $\mathbf{p}_{2}(t)=1-$ $t^{2} .$ Is $\left\{\mathbf{p}_{1}, \mathbf{p}_{2}\right\}$ a linearly independent set in $\mathbb{P}_{3} ?$ Why or whynot?

Linearly independent.

Calculus 3

Chapter 4

Vector Spaces

Section 3

Linearly Independent Sets; Bases

Vectors

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in this problem. We're given a set up for real, and we're basis. Uh, we're in space space formed by this Fulham's. So using this, people almost weakened. Sugar Petri is actually P one plus p too soapy. Three can be written as a linear combination off other two colonials. So spending said, hero, this face spent by old people in those you want me to be three the legal to the space spend by only using only Poland off you and Peter. Since Petri can be written as a communist off, you wanna pee too. And by looking at the person a second Hold on till we see that people and p two are we nearly dependent. So since they spend in space and since thoroughly new dependent on the basis for this system will be if you are and if you want and eat

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