(1 point) Select all of the vectors that are in the span of { ul , u2, u3 } . (Check every statem...
(1 point) Let u4 be a linear combination of {u1, U2, U3}. Select the best statement. O A. We only know that span{u1, U2, U3, u4} span{u1, u2, u3} . B. There is no obvious relationship between span{u1, U2, uz} and span{u1, U2, U3, u4} . C. span{u1, U2, U3} = span{u1, U2, U3, u4} when none of {u1, U2, uz} is a linear combination of the others. D. We only know that span{u1, U2, U3} C span{u1, U2, U3,...
(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement. OA. {u1, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OB. {ui, U2, U3, U4} is always a linearly dependent set of vectors. OC. {ui, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, U2, U3, U4} is a linearly...
(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best statement. A. {u1, U2, U3, U4} is never a linearly independent set of vectors. B. {U1, U2, U3, U4} is always a linearly independent set of vectors. C. {ui, U2, U3, U4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, 42, uz, u4} could be a linearly independent or linearly dependent set of vectors...
1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Below k The HW4: Problem 8 (1 point) Let u a and v Select all of the vectors that are in the linear combnations of (u, v (Check every statement tmat ts correct) @A. The vector?4 + 7?! t, a inear combraton or(u,v) B. The vechors a inear comtbination of (u,v) C.The veclor 7 nar cominaion of (u,v) E. All vectors in R are Inear combinations of the given vectors 9. The vectra-ainear contrat onor(mv) G. We cannot tell which...
(1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul , u2 , u3 and 14 are orthogonal. u1+ 7 U2 ll4 (1 point) 0 Given v 3 find the linear combination for v in the subspace W spanned by 0 0 3 3 and 114 , u2 = , из- 4 4 Note that ul...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
1 point) -3 Let A-3 4 14 and b- 12 -12 1 1 -4 -57 -24 Select Answer1. Determine if b is a linear combination of Ai, A2 and A3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation. (A non-trivial relation is three numbers that are not all three zero.) Otherwise, enter O's for the coefficients Ai+ A2t A, b. 1 point) Determine if the given subset of R3 is a...
vectors pure and applied. exercise 6.4.2 OIK IIC rather than Example 6.4.1 Let ul, u2 be a basis for F2. The linear map β : F., p given by is non-diagonalisable. hat β is diagonali able with respect to some basis. Then β would have Proof Suppose t matrix representation D=(d, 0 say, with respect to that basis and ß2 would have matrix representation 2 (d2 0 with respect to that basis. However for all xj, so β-0 and β2...
(1 point) Let H = span {v\,v2, v3, V4}. For each of the following sets of vectors determine whether H is a line, plane, or R3. Select an Answer 1. -2 -8 -6 28 2 8 6 28 , V3 = ,V4 3 13 10 46 2. Select an Answer 0 2 4 V2 , V3 4 = -3 0 -6 -12 Select an Answer 3. -1 7 -12 0 3 -7 -11 -1 , V2 = , V4 ,...