Vectores en R^2 y R^3, combinaciones lineales y aplicaciones a rectas y planos

Apuntes

S C I E N T I A E T TE C H N I C A P R O H V M A N I T A T E S V B L I B E R T A T I S T V T E L A -UTP- Universidad Tecnol´ogica de Pereira Facultad de Ciencias B´asicas Departamento de Matem´aticas Fecha: Taller de estudio: Vectores y operaciones. Rectas y planos. I. VECTORES EN R2 Y R3. (Excercises 1 to 3 taken from Kolman, Bernard and Hill, David. (2008). Elementary Linear Algebra with aplications. Ninth Edition. Pearson Education Inc. Pages 187 and 188.) 1. For what values of a and b or a, b and c, if possible, are the vectors #»u and #»v equal? a) #»u = [ a − b 2 ] , #»v = [ 4 a + b ] b) #»u = [ 2a − b a − 2b 6 ] , #»v = [ −2 2 a + b − 2c ] 2. Let #»u = [ 1 −2 3 ] , #»v = [−3 1 3 ] , #»w = [ r −1 s ] and #»p = [ 3 t 2 ] . If possible, find r, s and t, so that a) #»w = 1 2 #»u b) #»u = #»w + #»p c) #»v = #»w − #»u 3. Determine if #»u is a linear combination of the given vectors a) #»u = [−5 6 ] ; #»v 1 = [ 1 −2 ] y #»v 2 = [ 3 −4 ] . b) #»u = [ 2 −2 3 ] ; #»v 1 = [ 1 2 −3 ] , #»v 2 = [−1 1 1 ] y #»v 3 = [−1 4 −1 ] . 4. Determine los valores de α, si existen, de modo el vector #»u = [ 1 1 −1 ] sea combinaci´on lineal de los vectores #»v1 = [ 1 1 α ] y #»v2 = [ 2 α 4 ] . 5. Dete...