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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 47EQ
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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.

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.
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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