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 Aa 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. True C. There is a vector so that the set of solutions to is the z-axis. 1 True d. The solution set of a consistent inhomogeneous system Ar = b is obtained by translating the solution set of Ar 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 Aa 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. True C. There is a vector so that the set of solutions to is the z-axis. 1 True d. The solution set of a consistent inhomogeneous system Ar = b is obtained by translating the solution set of Ar 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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These were the Bartelby answers last time, this is not correct. Please correct this, thank you!
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 Aa,
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.
True
0.
C. There is a vector
so that the set of solutions to
is the z-axis.
1
True
d. The solution set of a consistent inhomogeneous system Ar = b is obtained by translating the solution set of Ar 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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