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midterm_fall_2009

# midterm_fall_2009 - Linear Algebra 1600a Midterm Last Name...

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Linear Algebra 1600a Midterm 7:00-10:00 pm October 30, 2009 Last Name First Name Student ID CIRCLE LECTURE AND LAB SECTIONS: 1 2 3 4 + 5 6 7 8 Σ 19 8 9 9 15 6 4 70 This exam has 11 problems on 8 pages. LECTURE: 001 MWF 8:30 002 MWF 10:30 LAB: 003 W 9:30 004 Th 2:30 005 Th 11:30 006 W 3:30 007 Th 12:30 008 W 11:30 NO CALCULATORS, NOTES OR OTHER AIDS. 1. For each of the following, circle T if the statement is always true and circle F if it can be false. (16 pts) If you are unsure, leave blank. Wrong answers will receive - 2 marks . (a) If A is a 3 × 4 matrix and b is in R 3 , then the system A x = b has infinitely many solutions. T F (b) If A is an invertible matrix, then the system A x = b has exactly one solution for every b . T F (c) For any m × n matrix A , the set of solutions to A x = 0 is a subspace of R n . T F (d) Every set of four vectors in R 3 is linearly dependent. T F (e) If A is a square matrix with two identical columns, then det( A ) = 0. T F (f) If A is skew-symmetric, then A T is symmetric. T F (g) λ = 1 is an eigenvalue of every square matrix A . T F (h) If u and v

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