1. Sketch the unit ball of a R²eWhen it is condowed with each of theBfollowing norms: bee ||il|I ||l`lla, ll·lly,and 11.1100. Sketch the ball of rading Iand contor (2, 1) in the matric determinedby each of these norms.

Answered: Image /qna-images/answer/429c1abb-cd08-4bc0-8254-6f5393450c3c.jpg

Answered: 1. Sketch the unit ball of the R² When…

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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D. Consider R³ with the metric i. Verify that d is really a metric. ii. State and prove the Bolzano-Weierstrass Theorem for R³ with this metric. Hint: Examine the proof for the complex numbers! d((x1, x2, x3), (V1, V2, y3) = |x1-y₁| + x2 - y2 + x3 - y3|.
b) The graph below shows dashed vector u and solid vector n. Draw projπ(n).
4. Determine whether the given vector is in the span(S) for the given set S. If it is not, write "Not in the span(S)". If it is, show or explain why it is in the span(S). a. v= (6, 2, 1, 11, 13); S = {(2,3, 1,6, 4), (3, 5, 1, 2, 3), (4, 2, 1, 5, 7), (3, 8, 2, 2, 1)} b. v=x4 – 3x³ + 4x² + 2x – 7; s = {p, r, s, t} where p = x+ - 3x3 + x2 – x + 1, r = 2x* – 3x2 + x + 3, s = x* + x³ + x² + 4x – 1 t = 3x* + x3 – 2x² + 3
2. Consider a metric in a D-dimensional space. Simplify the following expressions, i.e. the result may be a function of D, a simple tensor that you should identify, or even a vanishing one. a) g gup b) 9 9μ c) (VHV-g¹ V²)Vv d) g (AB-B₁A₂) e) guga (AB - 9μo 9upº Bº)
1-2- Find DCM for the following Euler angles using MATLAB: a- Rotation about the Z axis (Yaw angle - Psi) is 30 degrees b-Rotation about the Y axis (Pitch angle - Theta) is 20 degrees c-Rotation about the X axis (Roll angle - Phi) is 10 degrees Delivery date: until November 9th.
8. Let AB be the diameter of a circle with centre D. If C is any point on this circle prove (using vectors) that ZACB = 90° A D O В B

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1. Sketch the unit ball of the R² When it is condowed with each of the following norms: bee ||'117, llilla, Il·lly, and and 11:1100. Sketch the ball of rading I cantor (2, 1) in the metric determined by each of these norms.