b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. O A. 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 B. 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. OC. 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. O D. False. A nontrivial solution of Ax = 0 is the zero vector. Thus, a nontrivial solution x must have all zero entries. c. The effect of adding p to a vector is to move the vector in a direction parallel to p. Choose the correct answer below. O A. False. Given v and p in R? or R, the effect of adding p to v is to move v in a direction parallel to the line through v and 0. O B. False. Given v and p in R? or R, the effect of adding p to v is to move v in a direction parallel to the plane through v and 0. OC. True. Given v and p in R? or R°, the effect of adding p to v is to move v in a direction parallel to the line through p and 0. D. False. Given v and p in R2 or R³, the effect of adding p to v is to move v in a direction parallel to the plane through p and 0.
b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. O A. 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 B. 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. OC. 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. O D. False. A nontrivial solution of Ax = 0 is the zero vector. Thus, a nontrivial solution x must have all zero entries. c. The effect of adding p to a vector is to move the vector in a direction parallel to p. Choose the correct answer below. O A. False. Given v and p in R? or R, the effect of adding p to v is to move v in a direction parallel to the line through v and 0. O B. False. Given v and p in R? or R, the effect of adding p to v is to move v in a direction parallel to the plane through v and 0. OC. True. Given v and p in R? or R°, the effect of adding p to v is to move v in a direction parallel to the line through p and 0. D. False. Given v and p in R2 or R³, the effect of adding p to v is to move v in a direction parallel to the plane through p and 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:b. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below.
O A. 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 B. 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.
OC. 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.
O D. False. A nontrivial solution of Ax = 0 is the zero vector. Thus, a nontrivial solution x must have all zero entries.
c. The effect of adding p to a vector is to move the vector in a direction parallel to p. Choose the correct answer below.
O A. False. Given v and p in R? or R³, the effect of adding p to v is to move v in a direction parallel to the line through v
and 0.
B. False. Given v and p in R? or R, the effect of adding p to v is to move v in a direction parallel to the plane through
v and 0.
O C. True. Given v and p in R? or R³, the effect of adding p to v is to move v in a direction parallel to the line through p
and 0.
O D. False. Given v and p in R? or R³, the effect of adding p to v is to move v in a direction parallel to the plane through
p and 0.
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