Solution Found!
a. If × is a nontrivial solution of Ax = 0, then every
Chapter 1, Problem 24E(choose chapter or problem)
PROBLEM 24E
a. If × is a nontrivial solution of Ax = 0, then every entry in × is nonzero.
b. The equation × = x2u + x3v, with x2 and x3 free (and neither u nor v a multiple of the other), describes a plane through the origin.
c. The equation Ax = b is homogeneous if the zero vector is a solution.
d. The effect of adding p to a vector is to move the vector in a direction parallel to p.
e. The solution set of Ax = b is obtained by translating the solution set of Ax = 0.
Questions & Answers
QUESTION:
PROBLEM 24E
a. If × is a nontrivial solution of Ax = 0, then every entry in × is nonzero.
b. The equation × = x2u + x3v, with x2 and x3 free (and neither u nor v a multiple of the other), describes a plane through the origin.
c. The equation Ax = b is homogeneous if the zero vector is a solution.
d. The effect of adding p to a vector is to move the vector in a direction parallel to p.
e. The solution set of Ax = b is obtained by translating the solution set of Ax = 0.
ANSWER:
Solution (a) :
Step 1 : If × is a nontrivial solution of Ax = 0, then every entry in × is nonzero.
These may or may not exist. We can find out by row reducing the corresponding augmented matrix (A|0).