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(7 ifx # y to if x y Prove d(x, y) = is a metric on R (real numbers). (9 points) V.

(7 ifx # y to if x y Prove d(x, y) = is a metric on R (real numbers). (9 points) V.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION V
### Homework Assignment #### IV. Let \(\vec{x} = (-3, 1, 5, -2, 6) \in \mathbb{R}^5\). Find the norm of \(\vec{x}\), \(\| \vec{x} \|\), using the usual norm on \(\mathbb{R}^5\). (3 points) #### V. Prove \(d(x,y) = \begin{cases} 7 & \text{if } x \neq y \\ 0 & \text{if } x = y \end{cases}\) is a metric on \(\mathbb{R}\) (real numbers). (9 points) --- If you have any questions or need further clarifications on these problems, please feel free to ask your instructor. Happy studying!
Transcribed Image Text:### Homework Assignment #### IV. Let \(\vec{x} = (-3, 1, 5, -2, 6) \in \mathbb{R}^5\). Find the norm of \(\vec{x}\), \(\| \vec{x} \|\), using the usual norm on \(\mathbb{R}^5\). (3 points) #### V. Prove \(d(x,y) = \begin{cases} 7 & \text{if } x \neq y \\ 0 & \text{if } x = y \end{cases}\) is a metric on \(\mathbb{R}\) (real numbers). (9 points) --- If you have any questions or need further clarifications on these problems, please feel free to ask your instructor. Happy studying!
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