Which of the following statements is true about vectors in a vector space over a field ? A.A vector is called a linear combination of vectors in if is a scalar multiple of at least two vectors in . B.A vector is a linear combination of vectors in if spans every set of vectors that contain . C.A vector is a linear combination of the vectors in if the set of vectors is a linearly dependent set of vectors. D.None of the statements in this list is true. E. A vector is a linear combination of vectors in if is the sum of all the vectors in . .

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Answered: Which of the following statements is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which of the following statements is (are) false if all vectors are in R"? O aNot every orthogonal set in R" is linearly independent. O Statements a b and c O dThe orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv, where c is a non zero constant Statements b and c O None of the statements is false Obily is a linear combination of non zero vectors from an orthogonal set, then the weights in the linear combination can be computed with row operations on a matrix O di Uis ann x n orthogonal matrix, then the rows of U form an orthogonal basis of R O All the statements are false O Statements a, b and d Question
3.
12 1 -1 1 0 2 2 -2 20 4 3 -3 3 0 6 Let A = -4 4 40-8 5 -5 5 0 10 6 -660 8 Which one of the following is NOT true about Col(A)? Select one alternative: Col(A) is a vector space of dimension 3 Col(A) is a subspace of R Col(A) is the span of Col(A) is the span of 123 -4 5 6 -2 2 -3 3 4 -5 5 2 3 -4 4 5 5 6 123 , which row reduces to 2 H N 246 -8 10 8 6 -8 10 8 [1 0 0 0 0 [0 -1 0 0 0 0 1 0 0 0 0 0 1 0 000 0 000 0 000
True/False: If true, justify your answer. If false, modify the bracketed statement to make the sentence true. a. If Ax = b has a unique solution, then [Ax = 0 has no solution (inconsistent).] b. If Ax = b has infinitely many solutions, then [Ax = 0 must have a nontrivial solution.] c. If a nonzero vector v exists such that Av = 0, then [both Ax = 0 and Ax = b must have infinitely many solutions.]
please prove 3 and 4
D,E only please
A,B,C,D,E please
Give a step by step proof with as much detail as possible.
Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and un. Which of the following statements are then true about the vectors 0 and u.? (Select all that apply ) O The vector 0 + u, is not equal to u, +0 O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is not equal to 0. O The vector 0 + u, is equal to un O The vector 0 + u, is equal.to 0 O The vector 0 + u, is not equal to u,. Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + 0 # 0, which contradicts that u, must have an additive inverse. O The statement u, + 0 + 0 + u, which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, + 0 + 0, which contradicts that u, is an additive identity. The statement u, + 0 + u. which contradicts that 0…

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	A.	A vector is called a linear combination of vectors in if is a scalar multiple of at least two vectors in .
	B.	A vector is a linear combination of vectors in if spans every set of vectors that contain .
	C.	A vector is a linear combination of the vectors in if the set of vectors is a linearly dependent set of vectors.
	D.	None of the statements in this list is true.
	E.	A vector is a linear combination of vectors in if is the sum of all the vectors in . .