Tugas Kelompok ke-3 (Minggu 8 / Sesi 12) 1. Given three vectors u 1, 3, 0 , v 2,1, 1 and w 0, 2, 3 . Determine: a. b. c. d. 3u 4v 5w . Cosine of the angle between u and v . Orthogonal projection of v on w and vector component of v orthogonal to w . u v w and u v w . Are they same? e. u g v w . f. A vector that is orthogonal to both u and w . 2. Given three vectors v1 2, 1, 0 , v2 1, 0, 2 and v3 0, 2, 1 . a. Is v1 a linear combination of v2 and v3 ? Explain the reason. b. Find the value of x such that w 1, 2, x is a linear combination of v1 and v2 . c. Are v1 , v2 and v3 linearly independent? Explain the reason. d. Find the scalars 1 , 2 , 3 such that 1, 2,3 1v1 2v2 3v3 , if they exist. MATH6078 - Linear Algebra