Mark each statement as true or false. Remember that a mathematical statement is said to be true if it is true under all circumstances. a. The homogeneous system Ax = 0 has the trivial solution if and only if the system has at least one free variable. False b. If x is a nontrivial solution of Ax = 0, then every %3| entry of x is nonzero. False c. There is a vector so that the set of solutions to [1 0 1 is the z-axis. x2 1 0 X3 False d. The solution set of a consistent inhomogeneous system Ax set of Ax b is obtained by translating the solution = 0. True e. The equation Ax b is homogenous if the zero vector is a solution. False f. A homogeneous linear system is always consistent. True
Mark each statement as true or false. Remember that a mathematical statement is said to be true if it is true under all circumstances. a. The homogeneous system Ax = 0 has the trivial solution if and only if the system has at least one free variable. False b. If x is a nontrivial solution of Ax = 0, then every %3| entry of x is nonzero. False c. There is a vector so that the set of solutions to [1 0 1 is the z-axis. x2 1 0 X3 False d. The solution set of a consistent inhomogeneous system Ax set of Ax b is obtained by translating the solution = 0. True e. The equation Ax b is homogenous if the zero vector is a solution. False f. A homogeneous linear system is always consistent. True
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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Please help. I have received 2 wrong answers so far.
Transcribed Image Text:Mark each statement as true or false. Remember that a
mathematical statement is said to be true if it is true under
all circumstances.
a. The homogeneous system Ax = 0 has the trivial
solution if and only if the system has at least one free
variable.
False
b. If x is a nontrivial solution of Ax = 0, then every
entry of x is nonzero.
False
[b1
so that the set of solutions to
c. There is a vector
1
is the z-axis.
x2
1 0
x3
False
d. The solution set of a consistent inhomogeneous
system Ax
set of Ax
b is obtained by translating the solution
= 0.
True
e. The equation Ax
b is homogenous if the zero
vector is a solution.
False
f. A homogeneous linear system is always consistent.
True
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