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quiz1_S2005

# quiz1_S2005 - T p 1 1 P = 2 3 4 and T p 1-2 P = 2-2 3 Find...

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Name Class Time MATH 202 - QUIZ # 1 Due Friday, February 25 at 2PM at your instructor’s ofce Covers Chapter 1 and Chapter 2 o± the text Time: 60 minutes Please show all work. Books, notes, calculators, are not permitted on this quiz. As part o± your obligations under the Honor Code, do not discuss this quiz with anyone until a±ter the Friday 2PM deadline. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination.

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1. (10 points) Find the intersection of the three planes x + y + z = 3 2 x - y + 2 z = - 2 4 x + y + 4 z = 4 Interpret your answer geometrically.
2. (10 points) For what values of b does the matrix equation 1 1 1 2 7 7 4 9 b 2 x y z = 1 2 b + 1 have (a) in±nitely many solutions? (b) no solutions? (c) exactly one solution? (Justify your answers.)

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3. (10 points) Let T : R 2 R 3 be a linear transformation such that

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Unformatted text preview: T p 1 1 P = 2 3 4 and T p 1-2 P = 2-2 3 Find the matrix of T . 4. (10 points) (a) Find the matrix P for projection in R 3 onto the plane 2 x + y + 3 z = 0. (b) Find a nonzero 3 × 3 matrix B so that BP = 0. 5. (10 points) (a) Let v b be a nonzero vector and suppose that the system Avx = v b has at least 2 diferent solutions. Then show that the homogeneous linear system Avx = v 0 has at least one nonzero solution. (b) IF v b = vV 1 + 2 vV 2 and For A = [ vV 1 | vV 2 | vV 3 ] we have rreF A = 1 0-1 0 1-3 0 0 then ±nd all solutions to Avx = v b . (c) (True or ²alse — IF true, explain why. IF False, give a counterexample.) IF an n × n matrix A is invertible and A 2 = A , then A = I ....
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quiz1_S2005 - T p 1 1 P = 2 3 4 and T p 1-2 P = 2-2 3 Find...

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