Write each vector as a linear combination of the vectors in S. (Use si and s2,...
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 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
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)
Need help please Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S1, S2, and s3, respectively, for the vectors in the set.) S = {(3, 4), (-1, 1), (2, 0)} (0,0) = Express the vector si in the set as a linear combination of the vectors S2 and 53. $1 =
(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 = {(2, −1, 3), (5, 0, 4)}(a) z = (1, −3, 5)z= (______)s1 + (_____)s2(b) v = ( 8, − 1/4, 27/4)v = (___)s1+(___)s2(c) w = (4, -7, 13)w = (___)s1+(___)s2(d) u = (5,1,-1)u = (___)s1 + (___)s2
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
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...
Determine whether S is a basis for R. S = {(2, 4, 3), (0,4,3), (0, 0,3)} OS is a basis for R3 S is not a basis for R3. If S is a basis for R3, then write u = (6, 8, 15) as a linear combination of the vectors in S. (Use S1, S2, and sz, respectively, as the vectors in S. If not possible, enter IMPOSSIBLE.) us
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)}.