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Consider the set L = 2. a. Does L contain the 0-vector? b. Is L closed...
I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a....
I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a. Prove that D2 is a vector space under these two operations b. Consider the set of all n × n diagonal matrices: di 00 0 d20 0 0d under ordinary matrix addition and scalar multiplication. Generalize your proof and nota in (a) to show that D is a vector space under these two operations for anyn
I. Consider the set...
linear algebra do both drawing in part A and B 2. Consider the set and let...
linear algebra
do both drawing in part A and B
2. Consider the set and let addition and scalar multiplication be the standard operations on vectors in R2 (a) State a specific numerical example that shows that V is not closed under vector addition, then draw a sketch for your example, shading the region V, and drawing your example vectors and their linear combination with the parallelogram method that shows V is not closed under vector addition (b) Provide a...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.
Let be the set of third degree polynomials Is a subspace of ? Why or why not?...
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...
16. [0/1 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 4.1.002 Find the component form of the given vector....
16. [0/1 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 4.1.002 Find the component form of the given vector. v= – 5² +47 X y 3 2 х -6 -5 -4 -3 - 2 -1 Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set {xy): x 29,729) The set is a vector space. The set is not a vector space because it is...
Let H be the set of third degree polynomials Let H be the set of third...
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...
Vector Space closed under scalar multiplication but not under addition
I just need an example of a vector space that is closed under scalar multiplication but not under addition. That is all. Thanks for your wisdom.
linear algebra 2 part mcq part a part b H Let be the set of third...
linear algebra 2 part mcq
part a
part b
H Let be the set of third degree polynomials H = {ax + ax? + ax' | AEC) P3 why or why not? H Is a subspace of Select all correct answer choices (there may be more than one). a. H P3 is a subspace of because it can be written as the span of a subset of b. H is a subspace of because it contains only second degree polynomials...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x...
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,...
Solve the problem. Let H be the set of all polynomials having degree at most 4...
Solve the problem. Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether His a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy A: Contains zero vector B: Closed under vector addition C Closed under multiplication by scala His not a vector space, not dosed under multiplication to scalars His a vector space His not a vector space:not closed under vector...
I. Consider the set of all 2 × 2 diagonal matrices: D2 under ordinary matrix addition and scalar multiplication. a. Prove that D2 is a vector space under these two operations b. Consider the set of all n × n diagonal matrices: di 00 0 d20 0 0d under ordinary matrix addition and scalar multiplication. Generalize your proof and nota in (a) to show that D is a vector space under these two operations for anyn
I. Consider the set...
linear algebra
do both drawing in part A and B
2. Consider the set and let addition and scalar multiplication be the standard operations on vectors in R2 (a) State a specific numerical example that shows that V is not closed under vector addition, then draw a sketch for your example, shading the region V, and drawing your example vectors and their linear combination with the parallelogram method that shows V is not closed under vector addition (b) Provide a...
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.
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...
16. [0/1 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 4.1.002 Find the component form of the given vector. v= – 5² +47 X y 3 2 х -6 -5 -4 -3 - 2 -1 Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set {xy): x 29,729) The set is a vector space. The set is not a vector space because it is...
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...
linear algebra 2 part mcq
part a
part b
H Let be the set of third degree polynomials H = {ax + ax? + ax' | AEC) P3 why or why not? H Is a subspace of Select all correct answer choices (there may be more than one). a. H P3 is a subspace of because it can be written as the span of a subset of b. H is a subspace of because it contains only second degree polynomials...
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,...
Solve the problem. Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether His a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy A: Contains zero vector B: Closed under vector addition C Closed under multiplication by scala His not a vector space, not dosed under multiplication to scalars His a vector space His not a vector space:not closed under vector...
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