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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
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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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
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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