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Dr. J. Ramanathan Math 122: Elementary Linear Algebra Due: 14 January 2016 Problem Set A Assignment1 Problem 1. Solve (if possible) the following system of equations 2x − y = 3 x + y = −1 Include a well drawn graph that shows that above two lines and any points of intersection. Problem 2. Solve (if possible) the following system of equations 2x − y = 3 −4x + 2y = −1 Include a well drawn graph that shows that above two lines and any points of intersection. Problem 3. Solve (if possible) the following system of equations 2x − y = 3 −4x + 2y = −6 Include a well drawn graph that shows that above two lines and any points of intersection. Problem 4. Find the equation of the line parallel to 3x − 8y = 24 that passes through the point (−2, 1). Illustrate with a well drawn sketch. Problem 5. Find the equation of the line perpendicular to 3x − 8y = 24 that passes through the point (−2, 1). Illustrate with a well drawn sketch. 1 All problems are worth five points, unless otherwise specified. 1 Dr. J. Ramanathan Math 122: Elementary Linear Algebra Problem 6. Let a, b, c, d, s and t be real constants (whose values are unknown). Consider the system ax + by = s cx + dy = t i. Find the general formula for x and y in terms of a, b, c, d, s and t. Show all steps. ii. What condition on a, b, c and d needs to be satisfied so that the formulas in the previous part is valid? 2