MATH 1502 Study Guide - Midterm Guide: Parametric Equation, Triangular Matrix, Gaussian Elimination
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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. Practice test 3: consider the system of equations given below and determine whether they are consis- tent. 0 c determine whether the following set of vectors is linearly independent or not, 2. a find a parametric equation for the plane passing through the points: a = Find the matrix representation for f (cid:18) 2x + 2y (cid:18) 2y (cid:19) 0 zy d the following transformation is linear and f(1, 0, 1) : determine between which ri the following transformations act and determine whether they are linear or not. For those that are linear nd their matrix representation. Show all work. (a) f(x, y, z) = (cid:19) (b) f(x, y) =
