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assign8

# assign8 - Assignment#8 due Wednesday November 28m9 9:29 am...

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Unformatted text preview: Assignment #8 due Wednesday, November 28m9 9:29 am questions 34 & 35 Test, Section 7.1 54: 62: questions: , p. 4 Text, Section 7.2, p. 4 8. Denote the principal axes as well 10. Plot as well 12. Plot as well, 27, 28. Plus: 1. Let A be a rank 1 real symmetric matrix. Prove A can be written in the form Q":— 1T: {if ﬁe. FR“ 2 2. (a) If A is symmetric and invertible, show that A2 is positive deﬁnite. (b) If A = l: 3 § J, show that A2 is positive deﬁnite while A is not positive deﬁnite. (c) If A. is positive deﬁnite, show that Ak is positive deﬁnite for all positive integers k. (d) If A!“ is positive deﬁnite where k is odd, show that A is positive deﬁnite. 3. For each of the quadratic forms below identify the type of eonic it represents, and ﬁnd the equations of the principal axis. Find also the maximum and minimum values of the quadratic form subject to the constraint IIXH = l where x = (3:, y)T. (a) 9:32 — Say + 3312 (b) 8x2 + Gary 4. Sketch the conic section given by 2x2 ~— 72323; + 23y2 : —50 in the icy—plane. ...
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