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Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax=0, then every entry in x is nonzero. Choose the correct answer below. OA. The statement is false. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. ◄► B. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x cannot have any zero entries. C. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. O D. The statement is false. The only solution of Ax=0 is the zero vector. Thus, a nontrivial solution does not exist.

Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax=0, then every entry in x is nonzero. Choose the correct answer below. OA. The statement is false. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. ◄► B. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x cannot have any zero entries. C. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. O D. The statement is false. The only solution of Ax=0 is the zero vector. Thus, a nontrivial solution does not exist.

Advanced Engineering Mathematics
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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Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. O A. The statement is false. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. O B. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax= 0. Thus, a nontrivial solution x cannot have any zero entries. C. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax=0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. D. The statement is false. The only solution of Ax = 0 is the zero vector. Thus, a nontrivial solution does not exist. wrong
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. O A. The statement is false. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. O B. The statement is true. A nontrivial solution of Ax=0 is a nonzero vector x that satisfies Ax= 0. Thus, a nontrivial solution x cannot have any zero entries. C. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax=0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. D. The statement is false. The only solution of Ax = 0 is the zero vector. Thus, a nontrivial solution does not exist. wrong
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