Question 3 T Let S be the set of vectors in R2 which satisfy the property...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
Let H = Let H= 1 33x2+59'51) 5y 51), which represents the set of points on and inside an ellipse in the xy-plane. Find two specific examples scalar to show that H is not a subspace of R2. H is not a subspace of R2 because the two vectors 3 1 show that H is not closed under addition. (Use a comma to separate vectors as needed.) H is not a subspace of R2 because the scalar 4 and the...
Let be the set of third degree polynomials Is a subspace of ? Why or why not? Select all correct answer choices (there may be more than one). a. is not a subspace of because it is not closed under vector addition b. is a subspace of because it contains the zero vector of c. is not a subspace of because it is not closed under scalar multiplication d. is a subspace of because it contains only second degree polynomials e. is...
1 point) Let V R2 and let H be the subset of V of all points on the line-4x-3y-0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? | H does not contain the zero vector of V | 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and...
Let H be the set of third degree polynomials Let H be the set of third degree polynomials {ax + ax? + ax3 | DEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is not a subspace of P3 because it is not closed under scalar multiplication b.H is a subspace of P3 because it contains the zero vector of P3 c. H is not...
Let H be the set of third degree polynomials H = {ax + ax2 + ax aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). 0 a. H is a subspace of P3 because it contains only second degree polynomials 1b. H is a subspace of P3 because it can be written as the span of a subset of P3 OcH is not a subspace of P3...
Let H be the set of third degree polynomials H = {ax + ax? + ax? | aEC} is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is a subspace of P3 because it contains the zero vector of P3 b.H is a subspace of P3 because it is closed under vector addition and scalar multiplication c. H is a subspace of P3 because it can...
Let H be the set of third degree polynomials H = {ax + ax? + ax3 | DEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. A is a subspace of P3 because it contains the zero vector of P3 | b. H is not a subspace of P3 because it does not contain the zero vector of P3 c. H is not a subspace of...
Let H be the set of third degree polynomials H = {ax + ax? + ax? | aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is a subspace of P3 because it contains the zero vector of P3 b. H is a subspace of P3 because it is closed under vector addition and scalar multiplication Oc H is a subspace of P3 because it...
3. (12 pt) Suppose that S is the subset of R2 that contains all vectors on the two lines y = x and y = -2 s={[x] € R: y=x or y = -x} ER2: y = r or y=- (a) In each of the following parts (i)-(iii), either show the statements is true or give a counterexample to show that the statement is false. Clearly state TRUE or FALSE. Graphs of y = x and y = -1 may...