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Which of the following are true statements? If {y, z} is linearly dependent, then {x, y, z} is 'linearly dependent for any X. Every set containing a spanning set is again a spanning set. If {x, y, z} is linearly independent, then {y, z} is linearly independent. If all of X1, X2,..., Xk are nonzero, then {X1, X2,...,xk} is linearly independent. If {x, y} is linearly independent, then {x, y, x+y} is linearly independent. If one of X1, X2,..., x is 0, then {x, y, z} is linearly dependent. If {x, y, z} is linearly independent, then ax+by+cz = 0 for some a, b and c in R.

Which of the following are true statements? If {y, z} is linearly dependent, then {x, y, z} is 'linearly dependent for any X. Every set containing a spanning set is again a spanning set. If {x, y, z} is linearly independent, then {y, z} is linearly independent. If all of X1, X2,..., Xk are nonzero, then {X1, X2,...,xk} is linearly independent. If {x, y} is linearly independent, then {x, y, x+y} is linearly independent. If one of X1, X2,..., x is 0, then {x, y, z} is linearly dependent. If {x, y, z} is linearly independent, then ax+by+cz = 0 for some a, b and c in R.

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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Which of the following are true statements? If {y, z} is linearly dependent, then {x, y, z} is 'linearly dependent for any X. Every set containing a spanning set is again a spanning set. If {x, y, z} is linearly independent, then {y, z} is linearly independent. If all of X1, X2,..., Xk are nonzero, then {X1, X2,...,xk} is linearly independent. If {x, y} is linearly independent, then {x, y, x+y} is linearly independent. If one of X1, X2,..., x is 0, then {x, y, z} is linearly dependent. If {x, y, z} is linearly independent, then ax+by+cz = 0 for some a, b and c in R.
Transcribed Image Text:Which of the following are true statements? If {y, z} is linearly dependent, then {x, y, z} is 'linearly dependent for any X. Every set containing a spanning set is again a spanning set. If {x, y, z} is linearly independent, then {y, z} is linearly independent. If all of X1, X2,..., Xk are nonzero, then {X1, X2,...,xk} is linearly independent. If {x, y} is linearly independent, then {x, y, x+y} is linearly independent. If one of X1, X2,..., x is 0, then {x, y, z} is linearly dependent. If {x, y, z} is linearly independent, then ax+by+cz = 0 for some a, b and c in R.
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