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Suppose a linear transformation $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ has the property that $T(\mathbf{u})=T(\mathbf{v})$ for some pair of distinct vectors $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^{n} .$ Can $T$ map $\mathbb{R}^{n}$ onto $\mathbb{R}^{n}$ ? Why or why not?

cannot

Algebra

Chapter 2

Matrix Algebra

Section 3

Characterizations of Invertible Matrices

Introduction to Matrices

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

02:40

Suppose vectors $\mathbf{v…

03:34

Let $V$ be a real inner pr…

04:28

Let $T : \mathbb{R}^{n} \r…

03:39

Let $T$ be a one-to-one li…

05:13

Suppose $T$ and $S$ satisf…

06:54

Let $T$ be a linear transf…

04:32

02:44

Let $T : \mathbb{R}^{m} \r…

03:07

02:14

Suppose $T: V \rightarrow …

problem. We have no transformation from our end to our end. Now we're given the assumption that, um, tur t u is equal to TV for some distinctive actors view. And you wanna be so or son, you nice to be We have t view you cross TV. So that means this lean your transformation is not 121 by the commission off went to one transformation and further. Um, since we know linear transformation, T can be expressed as matrix a times the vector X and that way, uh, by our convertible matrix to your room. The negation Because, uh, Lena transformation is not one to why he's actually the negation off. Art has off our in veritable Mitchard's Kira. So it just applied it r f but its indication. So this means since we have, um, indication enough off after convertible Mitri here. Um, so this means a is not convertible. Okay? And that implies, um, telling your transformation X I've been to a axe. Is not I'm too. This this is the vacation off heart. Um, it's a part. I bye aren't high. Uh, I am t So that means that Lena transformation t cannot be. Cannot be on thio. Um are into our in. So that's our final conclusion

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In mathematics, the absolute value or modulus |x| of a real number x is its …

Suppose vectors $\mathbf{v}_{1}, \ldots, \mathbf{v}_{p}$ span $\mathbb{R}^{n…

Let $V$ be a real inner product space, and let $\mathbf{u}_{1}$ and $\mathbf…

Let $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ be a linear transformati…

Let $T$ be a one-to-one linear transformation from a vector space $V$ into $…

Suppose $T$ and $S$ satisfy the invertibility equations $(1)$ and (2), where…

Let $T$ be a linear transformation that maps $\mathbb{R}^{n}$ onto $\mathbb{…

Let $V$ be a real inner product space, and let u be a fixed (nonzero) vector…

Let $T : \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$ be a linear transformati…

Suppose $T: V \rightarrow W$ is a linear transformation and $\left\{\mathbf{…

06:49

Find an LU factorization of the matrices in Exercises $7-16$ (with $L$ unit …

01:53

Without using row reduction, find the inverse of$A=\left[\begin{array}{c…

02:56

Describe the possible echelon forms of the matrix. Use the notation of Examp…

02:48

Show that if $A B$ is invertible, so is $A$ . You cannot use Theorem 6$(\tex…

04:11

Exercises $42-44$ show how to use the condition number of a matrix $A$ to es…

02:25

$[\mathbf{M}]$ With $A$ and $B$ as in Exercise $41,$ select a column $\mathb…

06:03

For $A$ as in Exercise $12,$ find a nonzero vector in Nul $A$ and a nonzero …

02:16

Unless otherwise specified, assume that all matrices in these exercises are …

02:53

Suppose a linear transformation $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{…

10:49

Exercises $23-26$ display a matrix $A$ and an echelon form of $A .$ Find a b…

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