Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = (6, -7, 8, 6), (4, 6, -4, 1)} (a) (18, 43, -32, 0) -1 6 + 35 89 -14, 4 (b) V = 2. V = 1 23 -4, -14, 8 57 (c) W = 8 61 73 s X W = + 6 24 13 -2, 3 4 (d) Z = 4, | »2 + X
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector v- (-1,5). 2 marks] (c) Using your result for part (b) verify that w = u-prolvu is perpendicular to V. 2 marks] (a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector...
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4,1)} (a) u = (18, 43, -32,0) (b) v=(4,1, 75, -10, 13) (c) w=(-4,-14, 15, 15) (d) z= (12, -6, 9, 39)
Consider the following vectors. 9 0 6 0 Give the corresponding linear combination. (If an answer does not exist, enter DNE.) 1I Is the vector v a linear combination of the vectors u1 and u? O The vector v is a linear combination of u and u 2 The vector v is not a linear combination of u1 and u2- Consider the following vectors. 9 0 6 0 Give the corresponding linear combination. (If an answer does not exist, enter...
Write each vector as a linear combination of the vectors in S. (Use Si and s2, respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.) S = {(1, 2, -2), (2, -1, 1)} (a) z = (-3,-1, 1) (b) v = (-1, -5, 5) (c) w = (2,-16, 16) (d) u = (1,-6,-6) (d)
Write v as a linear combination of ui, uz, and U3, if possible. (If not possible, enter IMPOSSIBLE.) v=(4, -22, -9, -10), 41 = (1, -3, 1, 1), u2 = (-1, 3, 2, 3), U3 = (0, -2, -2, -2) U1 + uz + U3
Write each vector as a linear combination of the vectors in S. (Use si and s2, respectively, for the vectors in the set. If not possible, enter IMPOSSIBLE.) S = {(1, 2, -2), (2, -1, 1)} (a) z = (-4, -3, 3) 2 = -251 – 1s2 (b) v = (-1, -6,6) (c) w = (0, -20, 20) w =
Find a linear combination of vectors vi -(1,-1,0,3),v2 (3,1,2,2). v (-2,4,-1, 3) that is equal to vector t - (1,9, 3,-2). If it's impossible, enter all zeros Find a linear combination of vectors vi -(1,-1,0,3),v2 (3,1,2,2). v (-2,4,-1, 3) that is equal to vector t - (1,9, 3,-2). If it's impossible, enter all zeros
(1 point) -6 -3 Use Theorem 5.5.2 to write the vector v = -4 as linear combination of -3/V14 1/714 -2/V13 0/V13 -3/V182 -13/V182 uj = u2 = and uz = -2/V14 3/V13 -2/V182 Note that uj, uz and uz are orthonormal. V= uj + u2+ uz Use Parseval's formula to compute ||v1|?. ||5|12=
Without using row reduction, write the vector [1 2 3]^T as a linear combination of the vectors in the set S={(1,-1,0), (2,2,5), (-5,-5,4)}.