MATH 120 INTRO TO LINEAR ALGEBRA GRADE ASSIGNMENT 1 DUE: OCTOBER 10, 2017 DIRECTIONS You are to work on all problems. Please start each problem (not each part on a clean: page and put you name on each page. When grading, I separate the assignments in pages and grade them appropriately. You will have until 11:59 pm to submit your assignment as a single word or pdf document. DO NOT SEND JPEGs. 1.) Given vectors p, q, r and s below: p q r s Sketch a) p + 2q b) 2r - s + q c) Show that 2(r + q) = 2r + 2q 2.) Using the following unit measure and define the following vectors as t, u o o v as t = (4, 225 ), u = (5, 330 ) and v = ( 3, 90o). Let w = 2t - 3v + u a. Sketch w b.) Express w in polar form Given the following vectors in Rn - Space, use them in the problem 3 - 7 3 = 5 1 = 12 3 = 0 7 6 1 = 0 5 9 = 2 5 3 7 = = 7 11 3.) Find: a.) 4c - 2d b.) || h - 3m|| 4.) Find: a.) c f b.) 6 7f 4 = 7 1 12 = 3 1 1 5 1 5 c. ) d(g,f) c.) What type of angle is formed by h and m ? Given the following vectors in Rn - Space, use them in the problem 3 - 7 = 3 5 = 1 12 3 = 0 7 6 1 = 0 5 9 = 2 5 3 7 = = 7 11 4 = 7 1 = 12 3 1 1 5 1 5 5.) Find: a.) Pd g b.) Ph ( l + 2m) c.) Using vectors a and b, show that projections are not commutative. 6.) a.) Write the span{c, d, g}. 7.) Find a.) | h x l | b) Find w1,4,5 c.) f x g b.) Find , the angle between a and b. 1 2 8.) Given vectors x = 5 and y = 3 5 where x and y connect at point A. 1 5 4 0 7 form parallelogram ABCD, a) What is the area of the parallelogram? b) What is the measure of angle ABC c) If z corresponds to point C, find z