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Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}\right\}$ be a basis for a vector space $V .$ Explain why the $\mathcal{B}$ -coordinate vectors of $\mathbf{b}_{1}, \ldots, \mathbf{b}_{n}$ are the columns $\mathbf{e}_{1}, \ldots, \mathbf{e}_{n}$ of the $n \times n$ identity matrix.

$b_{1_{\mathcal{B}}}=\left[\begin{array}{l}{1} \\ {0} \\ {\vdots} \\ {0}\end{array}\right]=e_{1}$

Calculus 3

Chapter 4

Vector Spaces

Section 4

Coordinate Systems

Vectors

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:56

In mathematics, a vector (…

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01:29

Let $A$ be an $m \times n$…

06:44

Let $A=\left[\begin{array}…

17:50

Let $B$ be an $n \times n$…

01:34

Let $\mathcal{B}=\left\{\m…

01:15

02:29

Suppose $A$ is an $m \time…

07:21

Determine a basis for the …

07:00

01:21

Suppose the columns of a m…

03:57

If $A$ and $B$ are $n \tim…

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