Algebra Consider the following subsets of R2: C1 = {(2, ) ER: x + 2y <...
Consider the following subsets of R2:
C1 ={(x,y)∈R2 :x+y≤3,x≥0,y≥0}
C2 ={(x,y)∈R2 :4x+y≤4,x≥0,y≥0}
Algebra Consider the following subsets of R2. Draw a sketch of the intersection CinC2 and the union C1UC2. State whether each set is convex or not. If the set is not convex, give an example of a line segment for which the definition of convexity breaks down
Algebra Consider the following subsets of R2. Draw a sketch of the intersection CinC2 and the union C1UC2. State whether each...
Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.
Consider the set A = {(x,0) ER|XE R} in R2 with the vertical line topology. Find the limit points of A. Consider the set A = {(x,0) ERP |x E R} in R2 with the vertical line topology. Find the boundary of A. Consider the set A = {(x,0) ERP|X E R} in R2 with the standard topology. Find the boundary of A.
linear algebra
2. Which of the following subsets of Rare actually subspaces? Justify your answer in terms of the definition and properties of subspaces. (a) The vectors [x y z]" with x + 2y -z = 0. (b) The vectors [a b c]" with a + b + c = 3. (c) The vectors [a+2bb-3b]' where a, b are any real numbers, (d) The vectors [pr] where q.r are any real numbers and p20.
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
Which of the following systems are inconsistent? (a) x + 2y + z = 2 (b) x + y + z 0 2x+2y-z=0 (c) -2x2 + 10 25 x2 +2x3 r2 (d) ax + by =
I need help with these linear algebra problems. 1. Consider the following subsets of R3. Explain why each is is not a subspace. (a) The points in the xy-plane in the first quadrant. (b) All integer solutions to the equation x2 + y2 = z2 . (c) All points on the line x + z = 5. (d) All vectors where the three coordinates are the same in absolute value. 2. In each of the following, state whether it is...
Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a (b) Solve the initial value problem. y(t) = Find the critical value a0 exactly. a0 = (c) Describe the behavior of the solution corresponding to the initial value a0. For a0, the solution is y(t) =
and C2 in the xy-planedefined by the parametric equations Consider trajectories on two curves C1:x=t?, y=t? - <t<«. C2: x = 3t, y=t?, - <t<mo. These two trajectories are known to *intersect* at exactly two points. The origin (0,0) is one of them. And there is another one, which we'll call P. Find Pand select the choice below which gives the slope of the tangent line to the first curve at the point P. Note that only ONE of the...
Consider the following constraints and the corresponding graph below Constraint 1: 2x-y21 Constraint 2:x+2y S8 Constraint 3: x-3y 2-2 2x-y-1 4 x +2y 8 4 7 a. (3 points) Shade the feasible region in the graph provided above. b. (3 points) The objective function is Minimize 2x-3y. Mark the optimal solution(s) in the above graph Do not calculate the x and y coordinates at optimal solution(s). Draw the optimal objective function line through the optimal solution(s).