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.
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problems are worth five points, unless otherwise specified.
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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?
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