b. If x is a nontrivial solution of Ax-0, then every entry in x is nonzero. Choo

Question

b. If x is a nontrivial solution of Ax-0, then every entry in x is nonzero. Choose the correct answer below 0 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 O B. True. A nontrivial solution of Ax-0 is a nonzero vector x that satisfies Ax = O. Thus, a nontrivial solution x cannot have any zero entries. entries are zero. ° C. 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 zerd 0 D. False. A nontrivial solution of Ax 0 is the zero vector. Thus, a nontrivial solution x must have all zero entries.

Explanation / Answer

False. If x is not equal to the zero vector, and Ax = 0, then x is a nontrivial solution. The trivial solution has all entries 0. If some entries are zero but not all, then x is not = 0.

Option c is the answer

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