(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) 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,...
12 points Let L: R3 → R3 defined by L U2 (1 3 57 rui 1 2||uz. Find ker L and dim ker L. LO 2 3] [u be your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after it the test.
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
R3 defined by 2. Let L be the linear operator on X21 X3X2 [x3- X1 L(x) and let S Span((1, 0, 1)) (a) Find the kernel of L (b) Determine L(S) (c) Determine L(R3). jes (d) Is L an onto mapping?
Let Ui and U2 be independent random variables, each one distributed uniformly on Z be the minimum, Z = min{U1, U2} and W be the maximum, W = max{U1, U2}. Find the joint p.d.f of Z and W [0, 1]. Let Let Ui and U2 be independent random variables, each one distributed uniformly on Z be the minimum, Z = min{U1, U2} and W be the maximum, W = max{U1, U2}. Find the joint p.d.f of Z and W [0,...
Q4. Let L: R2 + Rº be a transformation defined by L (0-2 [3u2 – U1 U1 – U2 -502 (a) Show that I is a linear transformation. (b) Find the standard matrix A of L, and find L ([31]) using the matrix A. (c) Do you think that any transformation T:R2 + R² is linear? (Justify your answer).
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
4. (a) L ,DER et a i. Let U1 be the set of solutions for the equation For which values of a and b is U1 a subspace of R4? ii. Let U2 be the set of solutions for the equation For which values of a and b is U2 a subspace of R4? iii. Let U3 be the set of solutions for the equation For which values of a and b is Us a subspace of R4? Justify your...
(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...