Determine if it is true or false. Please justify. O 02- y "The set S= 0...
Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. True by the definition of a vector space O B. False; not all vectors are elements of a vector space. O C. False; a vector space is any element of a vector. b. If u is a vector in a vector space V, then (-1) is the same as the negative...
linear algebra question easy, please answer fast with steps
Mark each statement True or False. Justify each answer. Here A is an mxn matrix. Complete parts (a) through (e) below a. If B is a basis for a subspace H, then each vector in H can be wrben in only one way as a linear combination of the vectors in B. Choose the correct answer below O A. The statement is false. Bases for a subspace H may be linear...
Determine whether each statement is True or False. Justify each answer a. A vector is any element of a vector space. Is this statement true or false? O A. False; a vector space is any element of a vector O B. True by the definition of a vector space O C. False; not all vectors are elements of a vector space. b. If u is a vector in a vector space V, then (-1)u is the same as the negative...
Question 1 (10 Marks) This question consists of 10 true false ansers. In cach ease, answer true if the statement is always true and false otherise. If a statement is false, 1. The set rER0 isa group under the binary operation o defined ad-be is a group under matrix addition. 3. Tho sot eRzs not an Abelian group under the binary erplain why. There is no need to show working for true statements. by a ob vab. 2. The set...
please explain.... Thank You
(1) What is the dimension of the space R6? (m) Let T : R5 → R. Is it true or false that the null space of T is a subspace of R4? (n) Let T: R3R5. I f R5? s it true or false that the range of l' is a subspace o (o) Find a basis for the span of the set of vectors012
(1) What is the dimension of the space R6? (m) Let...
6.2.24 Justify each Assume all vectors are in R. Mark each statement True or False. Justify each answer a. Not every orthogonal set in Rn is linearly independent. O A. False. Orthogonal sets must be linearly independent in order to be orthogonal. O B. True. Every orthogonal set of nonzero vectors is linearly independent, but not every orthogonal set is linearly independent. O C. False. Every orthogonal set of nonzero vectors is linearly independent and zero vectors cannot exist in...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
(a) State whether the following statement is true or false. The follow set is a subspace of P2, where P2 is the set of all polynomials over the real numbers of degree 2 or less. W={p € P2 :p (3)=0} O True O Fale In the essay box below, if it is true, prove that W is closed under scalar multiplication. Otherwise, give an explantion why the statement is false. XDX HE Editor A-AIBIU S *** Styles Font Size Words:...
2. Determine each of the following statement is true or false and justify your answer: (a) S has a subgroup of order 15. (b) S5 has a subgroup of order 40
2. Determine each of the following statement is true or false and justify your answer: (a) S has a subgroup of order 15. (b) S5 has a subgroup of order 40
Determine whether the set together with the standard operations
is a subspace of M2,2. Justify the answer:
Determine v nine whether the set, together with the standard opera andard operations 1 b 1, where a, b and c are real numbers perations is a subspace of M. You your answer. This is for parts a) and b) only a) The set of all 2 by 2 matrices of the formla (5 points) andarderations is a subspace of M The set...