HW1

MATH 2418: Linear Algebra Assignment# 1 Due :08/29, Tuesday, 11:59pm Term :Fall 2023 [Last Name] [First Name] [Net ID] [Lab Section] Recommended Problems: (Do not turn in) Sec 1.1: 1, 2, 3,4,5, 8, 9, 10, 11, 12, 13, 14, 15,17, 18,19,25, 26, 27. 1. Let v = ( 2 , - 3 , 1 ) , w = ( 1 , - 1 , 1 ), and 3 u - 2 v - 4 w = ( - 1 , 2 , 3). Find (a) the vector u (b) the linear combination: - 2 u + 3 v + 5 w . 1

2. Given vectors v and w in diagram below, shade in all linear combinations c v + d w for (a) 0 ≤ c ≤ 1 and 0 ≤ d ≤ 1 (b) 0 ≤ c ≤ 1 and d > 1 (c) 0 ≤ d ≤ 1 and c > 1. (You can use different shading styles in same picture for all three parts or can graph them separately in three different pictures) x y v w 2 / 6

3. Let 0 = (0 , 0 , 0) , i = (1 , 0 , 0) , j = (0 , 1 , 0) , k = (0 , 0 , 1) be vectors in R 3 . Given a cube with an edge 2 inch the figure below O y z x C D B A E F G (a) Write down the vectors --→ OG, --→ OD, --→ OE, --→ OF as linear combinations of i , j , k . (b) Let P, Q, R, S, T, U be center of the faces AGFE, GBDF, DCEF, OAEC, OAGB, OBDC respec- tively, write the vectors: --→ OP, --→ OQ, --→ OR, -→ OS, -→ OT, --→ OU as a linear combination of i , j , k . 3 / 6