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$\mathcal{B}$ and $\mathcal{C}$ are bases for a vector space $V$ Mark each statement True or False. Justify each answer.a. The columns of the change-of-coordinates matrix $c \leftarrow \mathcal{B}$ are $\mathcal{B}$ -coordinate vectors of the vectors in $\mathcal{C}$ .b. If $V=\mathbb{R}^{n}$ and $\mathcal{C}$ is the standard basis for $V,$ then $c \leftarrow \mathcal{B}$ is the same as the change-of-coordinates matrix $P_{\mathcal{B}}$ introduced in Section $4.4 .$

A. FalseB. True

Calculus 3

Chapter 4

Vector Spaces

Section 7

Change of Basis

Vectors

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Okay, so for problem 12 we need to identify statement a first to call himself the columns of the change. According the Matrix from B to see Arlene Odie independent, whether this is short balls. So, uh, so this statement is true. The reason this is stated in our textbook and excess. So to call himself off the change of corn and a matrix frumpy to see our linearly independent because they are the coordinates vectors off the we nearly independent set off. So how just marked the page number so you can check this out. Page page 2 28 Okay. So Steam and B says if the d take the view to be are too And, uh, the basis is we won't be too. And, uh see wants you to. So the real reduction Upsy once you do you want me to to I and P produces it to reduce its ah metrics. P that satisfy said it's 56 b p x c. So one thing to notice here is that misty mate says for all specter eggs in the But this is impossible. So why it is impossible. I'll try now. Explain the eight and the next page. So first, by our equation, giving the textbook we have can t the change of corn The matrix to BC to be the change of quantum matrix from Peter to see Then we have, ah record reckon X under B is equal to universe uh, Bracket C So he in first it's the Patriots that satisfied is he this equation? And by overthere, um 16 in a textbook that implies, Yeah, p it's not always the case. He is equal to P. Ah, yeah, this Now it's not always the case that the inverse of peace you got to pee. So this statement is wrong.

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