3105_S10_midterm1

# 3105_S10_midterm1 - (b(5 points Deﬁne a ﬁeld with three...

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EEL4834 Midterm 1 10/06/2009 Answer the questions in the space provided on the sheets. Show all work. If you run out of space, write on the back of the page. PLACE A BOX AROUND YOUR FINAL ANSWER . Answers not clearly marked may not be graded. Student name and UFID: Question: 1 2 3 4 5 Total Points: 30 10 15 25 10 90 Score: 1. Some soft-balls: (a) (5 points) The syntax for a vector in Matlab is { 0 1 2 } , True or False? (b) (5 points) Every element in a ﬁeld has a multiplicative inverse, True or False? (c) (5 points) If z = a + ib for real a,b then | z | 2 = a 2 + b 2 , True or False? (d) (5 points) | ~a × ~ b | = sinθ | ~a || ~ b | where θ is the angle between ~a, ~ b , True or False? (e) (5 points) Every linearly depedent set of vectors is a basis, True or False? (f) (5 points) If A is a 3 × 2 matrix, B is a 2 × 4 matrix, then BA is well deﬁned and is 3 × 4, True or False? 2. Groups and Fields (a) (5 points) What the diﬀerences between a group and ﬁeld?
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Unformatted text preview: (b) (5 points) Deﬁne a ﬁeld with three elements: 0 , 1 ,ω . 3. Complex Numbers Consider z = 3-4 i . (a) (5 points) Compute | z | . (b) (5 points) Compute the real and imaginary parts of 1 /z . (c) (5 points) Write z in polar form. 4. Bases Consider v 1 = [1 2 i 3] v 2 = [2 3 1]. (a) (5 points) Compute v 1 · v 2 . (b) (5 points) Compute | v 1 | 2 (c) (5 points) Show that v 1 and v 2 are linearly independent. (d) (10 points) Use v 1 and v 2 to build an orthonormal bases. 5. Matrices Consider A = ± 5 2 7 2 9 8 ² and B = 2 3 5 7 11 13 (a) (5 points) Compute AB if it is valid, or state invalid. (b) (5 points) Compute BA if it is valid, or state invalid. Page 1 of 1...
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