Math 230 Exam 1

Math 230 Exam 1 - Honors Introductory Linear Algebra(Math...

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Honors Introductory Linear Algebra (Math 230) – Spring 2011 Midterm Examination There are eight problems and six pages in this exam. Provide appropriate justifications where required. Total points given in parentheses add to 105. You will be graded for 100 points. 1. (12) Find the matrix of the linear transformation T : R 4 R 2 that first projects points in R 4 to R 2 by ignoring the 3rd and 4th coordinates, then horizontally shears the resulting vectors such that e 2 R 2 is mapped to e 2 + 2 e 1 , while leaving e 1 unchanged, and then reflects the vectors thus obtained through the vertical axis. 2. (19) Consider the following system of linear equations. x 3 + x 4 + x 1 = 1 - 4 x 4 + x 2 = 0 - 2 x 1 + 2 x 2 - x 3 - x 4 = 3 (a) Write the system as a vector equation. (b) Write the system as a matrix equation A x = b . (c) Solve the system by reducing its augmented matrix to reduced row echelon form. Write the general solution to the system in the parametric-vector form.

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