In the following augmented matrices x is a real parameter and they are obtained in the process of verifying if a vector b belongs to V = Gen{a1, a2, a3}. Indicate in each case how one should answer with respect to the following categories: 1) For every value of x the vector b does not belong to V. 2) There is only one value of x for which vector b does not belong to V. 3) There is only one value of x for which vector b belongs to V. 4) For every value of x the vector b belongs to V.
In the following augmented matrices x is a real parameter and they are obtained in the process of verifying if a vector b belongs to V = Gen{a1, a2, a3}. Indicate in each case how one should answer with respect to the following categories: 1) For every value of x the vector b does not belong to V. 2) There is only one value of x for which vector b does not belong to V. 3) There is only one value of x for which vector b belongs to V. 4) For every value of x the vector b belongs to V.
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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Question
In the following augmented matrices x is a real parameter and they are obtained in the process of verifying if a
Indicate in each case how one should answer with respect to the following categories:
1) For every value of x the vector b does not belong to V.
2) There is only one value of x for which vector b does not belong to V.
3) There is only one value of x for which vector b belongs to V.
4) For every value of x the vector b belongs to V.
Transcribed Image Text:En las matrices aumentadas siguientes x es un parámetro real y ellas son
obtenidas en el proceso de verificar si un vector b pertenece a V = Gen{a1,
a2, a3}
a)
b)
1 4
-3
2
0-2
4
3
0 0 1+ 4x 4+ 16 x
3
-3
0 0 4+x
3
2
0 -1
0
1
-1 R:
R:
Indique en cada caso cómo se debe responder respecto a las siguientes
categorías:
1) Para todo valor de x el vector b no pertenece a V.
2) Sólo hay un valor de x para el cual el vector b no pertenece a V.
3) Sólo hay un valor de x para el cual el vector b pertenece a V.
4) Para todo valor de x el vector b pertenece a V.
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