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 vec...
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)
O Determine if b is a linear combination of the vectors formed from the columns of the matrix A. 4 A= 1 - 6 3 0 2 4 -4 24 - 12 b= -6 -4 Choose the correct answer below. O A. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. OB. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots...
VECTOR SPACES LINEAR ALGEBRA Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication operations on u = (u1, u2) and v = (v1, v2): u + v = (u1 + v1 + 1, u2 + v2 + 1), ku = (ku1, ku2) a) Show that (0,0) does not = 0 b) Show that (-1, -1) = 0 c) Show that axiom 5 holds by producing an ordered pair -u...
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)
How does one solve this problem? 4. (a) Consider the vector space consisting of vectors where the components are complex numbers. If u = (u1, u2, u3) and v = (V1,V2, us) are two vectors in C3, show that where vi denotes the complex conjugate of vi, defines a Hermitian (compler) inner product on C3, i.e. 1· 2· 3, 4, (u, v) = (v, u), (u+ v, w)=(u, w)+(v, w), (cu, v) = c(u, v), where c E C is...
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
Consider the following function. (If an answer does not exist, enter DNE.) 5 6 f(x) = 1 + х x² (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x=0 Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.) 1 y = (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) (-00,0) U( 13.00) X Find the interval where the function is decreasing. (Enter your answer using interval notation.)...
9 -4 0 0 A4 5 2 0 0 0 1 2 and consider the vector space R4 with the inner product given by v, w)Aw. Let 0 0 -2 and let W span(Vi, V2, V3 ). In this problem, you will apply the Gram-Schmidt procedure to vi, v2, v3 to find an orthogonal basis (u, u2, u31 for W (with respect to the above inner product). b) Compute the following inner products. (v2, u1) - Then u2 =Y2__v2.ul) ui,...
Determine if b is a linear combination of the vectors formed from the columns of the matrix A. 1 5 5 2 A= 0 6 3 b -5 -4 20 - 20 - 2 Choose the correct answer below. O A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the...
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