# Practice Test 3

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Georgia Institute of Technology

Mathematics

MATH 1502

Geronimo

Fall

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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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