Homework - Linear Algebra Basics 1. From 17 : l i J and } : l i I, nd the components of 317 + \"113 and or? + (if). . How long is the nine-dimensional vector '3\" : [1, 1, 1, ...]? Find a unit vector 11' in the same direction as 17 and a unit vector '13 that is perpendicular to if. . Compute As: for the following two paris of matrices using (a.) dot products with the column vector and (b.) as a combination of the columns: 124 2 231 2 412 3 2100 1 1210 1 01211 0012 2 c. How many individual multiplications are performed to nd As; when the matrix is "3 by 3"? . Solve the system of equations using elimination and book substitution. Circle the pivots. 2:1: 3y : 3 4a: 5y +2 : 7 23: y 3z : 5 . Find the inverse matrices A'1 and B1 (if they exist) by elimination on [A I] and[BI]: 2 1 1 2 1 1 A: 1 2 1 ,B: 1 2 1 1 1 2 1 1 2 . Find the complete (or 'Lgeneml") solution to the following equation: 1112 f 1 2648 9:3 0024: 1 1 1 1 0 0 _1 ,v2: 0 3'03: 0 '04: 1 ,v5* 1 {05* 0 1 0 1 0