Practice Test 3

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School
Georgia Institute of Technology
Department
Mathematics
Course
MATH 1502
Professor
Geronimo
Semester
Fall

Description
Math 1502 Practice Test 3 Geronimo ˜ 1.a) Let A be a 4 × 4 matrix and A be a matrix in echelon form obtained from A by row reduction. Show that A is either an upper triangular matrix with nonzero diagonal entires, or the last row must be a row of zeros. b) Consider the system of equations given below and determine whether they are consis- tent. If so find all the solutions.         1 2 1 2 0 1 2 1 0   ¯     ¯   i) A = 2 0 1 b = 1 , ii) A = 1 2 0 1 b = 1 . 3 2 2 0 1 4 2 0 3 2.a Find a parametric equation for the plane passing through the points,       1 2 3 ¯ =  0 ¯ =  1 ¯ =  1 . 1 2 3 1 0 1   2 1 2 1   b Let A = 0 2 3 , and x = 1 . Find Ax. 3 c Determine whether the following set of vectors is linearly independent or not,  1  3  1
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