a. The homogeneous system Ax solution if and only if the system has at least one free = 0 has the trivial variable. Choose b. If æ is a nontrivial solution of Ax = 0, then every entry of x is nonzero. Choose c. There is a vector so that the set of solutions to X1 [1 x2 [0 1 0] x3 is the z-axis. b2 Choose
a. The homogeneous system Ax solution if and only if the system has at least one free = 0 has the trivial variable. Choose b. If æ is a nontrivial solution of Ax = 0, then every entry of x is nonzero. Choose c. There is a vector so that the set of solutions to X1 [1 x2 [0 1 0] x3 is the z-axis. b2 Choose
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: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.
Choose
b. If x is a nontrivial solution of Ax = 0, then every
entry of x is nonzero.
Choose
c. There is a vector
so that the set of solutions to
[1
X2
is the z-axis.
x3
Choose
d. The solution set of a consistent inhomogeneous
system Ax
set of Ax = 0.
b is obtained by translating the solution
Choose
e. The equation Ax
b is homogenous if the zero
vector is a solution.
Choose
f. A homogeneous linear system is always consistent.
Choose
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