Math Midterm 1 (#2).pdf

X 1 x 2 3 x 3 1 2 x 1 x 2 3 x 3 3 x 1 x 2 tx 3 1 b 2

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x 1 - x 2 - 3 x 3 = 1 2 x 1 - x 2 - 3 x 3 = - 3 x 1 - x 2 + tx 3 = 1 (b) [2 points] Write down the general solution of the linear system for the value of t that you find in part (a). Page 5 of 8
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Student # MAT 1302A First Midterm Exam 5. [3 points] Consider the vectors u = 1 2 2 - 1 2 , v 1 = 2 - 2 4 - 1 , v 2 = 1 - 4 2 - 1 2 , v 3 = - 2 7 - 4 2 Determine if u belongs to Span { v 1 , v 2 , v 3 } . Page 6 of 8
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Student # MAT 1302A First Midterm Exam 6. [3 points] For each of the following statements, indicate if it is true or false . You will receive 1 point for every correct answer and lose .5 points for every incorrect answer (but you cannot receive a negative mark on this question). (a) A consistent linear system with 5 equations and 5 variables always has a unique solution. (b) If the span of two vectors v , w R 3 is a line, then there exists a scalar c R such that v = c w or w = c v . (c) If A is a 4 × 5 matrix and x = x 1 x 2 x 3 x 4 x 5 then the homogeneous linear system A x = 0 has infinitely many solutions. Page 7 of 8
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Student # MAT 1302A First Midterm Exam This page is intentionally left blank. You may use it as scrap paper. Page 8 of 8
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  • Fall '19
  • Vector Space, Department of Mathematics and Statistics, Hadi Salmasian, number of points

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