1. For the 3-node triangular graph in the figure following, write the 3 by 3 incidencematrix A. Find a solution to Ax = 0 and describe all other vectors in the nullspace ofA. Find a solution to A¹y = 0 and describe all other vectors in the left nullspace ofA.edge 1node 2node 1edge 2edge 3node 3x2Y1Y4x1Y5X4Y3Y6Y2x3

Answered: 1. For the 3-node triangular graph in…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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For the following matrix, find the vectors which span NulA.
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b. where 17. Consider a matrix A of the form A -a a? + b? v and w such that Av entries of v and w in terms of a and b). Conclude that T(x) spanned by v. = 1. Find two nonzero perpendicular vectors = i and Aw = -w (write the = Ax represents the reflection about the line L nst ni
2. In a dance performance, four dancers form a diamond with vertices A(2, 0), B(0, 2), C(-2, 0), and D(0, – 2). Then, they move along the dance floor following the translation vector, (0, 4). There they pause, and then move again along the same vector. What are their coordinates after six such translations? а. А(26, 24), В'(24, 6), С'(22, 24), аnd D'(24, 22) b. A'(2, 10), B'(0, 12), C'(-2, 10), and D'(0, 8) c. A'(2, 24), B'(0, 26), C'(-2, 24), and D'(0, 22) d. A(26, 0), B' (24, 2), С'(2, 0), and D'(24, - 2) Name: ID: A
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1.3 Find the area of the parallelogram with the vertices A(-5, -4), В(2, —4), С(4,4) and D(-3,4). Use vectors to decide whether the triangle with vertices P(1,–3,–2), Q(2,0, –4) and R(6, – 2, –5) is right-angled. For what values of b are the vectors and orthogonal? 1.6 Find the vector projection, ProjgA and ProjĄB When A = i+ 2j + k and B = k. Get Gmail for 1.4 mobile 1.5 2j=k in terms. 11:27 AM a-i+j, b=-1+j, . 10:32 AM your guide to 10:29 AM 10:28 AM
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6. Show that the points A, B and C with position vectors d = 3î – 4) – 4k, 6 = 2î – ĵ + k and č = i – 33 – 5k, respectively form the vertices of a right-angled triangle.
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