MATH 33AH Study Guide - Final Guide: Qr Decomposition, Parallelepiped
Document Summary
The nal exam is cumulative and will cover all the material in the lectures. Your review should, therefore, include the information on the study guides for each of the rst two midterms. Also chapter 7 and crucial ideas from chapter 8 will be fair game. The actual nal exam will consist of problems that are related to the ones below. Indicate whether there are zero, one, or in nitely many solutions. x1 + 2x2 + 3x3 + x4 = 1. 2x1 + x2 x3 + 4x4 = 2. 7x1 + 5x2 + 13x4 = 7 (b) find the inverse of the matrix. 0 3/2 1/2 (c) describe the matrix in the second part geometrically: for the following matrix. 1 (a) find rref(a). (b) find a basis for im(a) (c) find a basis for ker(a: consider the system a~x = ~0 where where t is any real number.
