MATH 551 Midterm: MATH 551 KSU S14 Test2 Practice
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15 Feb 2019
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You may use other side of the sheet if you need more space. Problem 1 [10 points] find the coordinates of the vector v in the orthogonal basis b = {v1, v2}: v1 = (cid:18) 2. Problem 2 [10 points] find the orthogonal projection of v onto the line l de ned by u: u = (3, 2, 1, 1), v = (1, 1, 0, 0). Problem 3 [10 points] state whether the following is true or false and explain your answer: the columns of the matrix a span r3: Problem 4 [10 points] find a matrix of the linear transformation t . Find the kernel ker t and the range ran t : T (x1, x2) = (2x1 2x2, x1 + x2). Problem 5 [20 points] find the bases for the null space, column space and row space of a matrix: verify that nullitya + ranka = n, where n is a number of columns in the matrix a:
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