1 Sea f:V\342\206\222V' la aplicaci\303\263n lineal tal que f(x)= Mx ,M=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 a) Halla ecuaciones cartesianas, ecuaciones param\303\251tricas y un base del subespacio vectorial Im(f) b) Halla ecuaciones cartesianas, ecuaciones param\303\251tricas y un base del subespacio vectorial Ker(f) c) Clasifica f d) Sea el vector u=(1,-1,3,3). Describe el conjunto de los vectores x tales que u=f(x) e) Sea B'\342\204\2353={(1,4,1), (-5,3,2),(0,1,-3)} una base de \342\204\2352 y B'\342\204\2354={(1,1,0,0),(1,0,-1,2),(2,0,0,3),(1,2,0,-1)} una base de \342\204\2353 Halla la matriz de f en las base B'\342\204\2353 , B'\342\204\2354 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSV3aXRoRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEnbGluYWxnRidGL0YyRjlGNQ== PkkiTUc2Ii1JJ01hdHJpeEdGJDYjL0kkJWlkR0YkIiopZW5NOg== LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKillbk06 LUklcmFua0c2IjYjSSJNR0Yk IiIj LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= a) Base de la imagen de f BIm(f)={(1,-1,2,0),(0,0,1,3)} es una base de la imagen PkkieUc2Ii1JJmV2YWxtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomSSZhbHBoYUdGJCIiIjcmRi4hIiIiIiMiIiFGLkYuKiZJJWJldGFHRiRGLjcmRjJGMkYuIiIkRi5GLg== PTYiNiM7IiIiIiIlRVxbbCVGJkkmYWxwaGFHRiMiIiMsJEYpISIiIiIkLCZGKUYqSSViZXRhR0YjRiZGJywkRi9GLQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= Ecuaciones param\303\251tricas QyovLiZJInlHNiI2IyIiIkYlRikvLiZGJjYjIiIjRixGKS8uJkYmNiMiIiRGMUYpLy4mRiY2IyIiJUY2Rik= LyZJInlHNiI2IyIiIkkmYWxwaGFHRiU= LyZJInlHNiI2IyIiIywkSSZhbHBoYUdGJSEiIg== LyZJInlHNiI2IyIiJCwmSSZhbHBoYUdGJSIiI0klYmV0YUdGJSIiIg== LyZJInlHNiI2IyIiJSwkSSViZXRhR0YlIiIk QyQ+SSNNMUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjL0kkJWlkR0YlIipLKm9NOiIiIg== LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKksqb006 Ly1JJGRldEc2IjYjLUkqc3VibWF0cml4R0YlNiVJI00xR0YlOyIiIiIiJEYrIiIh LywmJkkiekc2IjYjIiIjISIiJkYlNiMiIiJGLCIiIQ== Ly1JJGRldEc2IjYjLUkqc3VibWF0cml4R0YlNiVJI00xR0YlOyIiIyIiJTsiIiIiIiQiIiE= LywoJkkiekc2IjYjIiIlIiIiJkYlNiMiIiQhIiQmRiU2IyIiIyIiJyIiIQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= son las ecuaciones cartesianas de la imagen de f La aplicaci\303\263n no es sobreyectiva porque dim(Im(f)) no es 4, no es inyectiva porque la dimensi\303\263n del n\303\272cleo es 1 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= b) Estudia el n\303\272cleo Mx=0, Mx=b PkkiYkc2IjcmIiIhRiZGJkYm NyYiIiFGI0YjRiM= Ecuaciones cartesianas QyQtSSVyYW5rRzYiNiNJIk1HRiUiIiI= IiIj JSFH PkkjTTJHNiItSSpzdWJtYXRyaXhHRiQ2JUkiTUdGJDckIiIiIiIlO0YqIiIk PTYiNiQ7IiIiIiIjO0YmIiIkRVxbbCc2JEYmRilGKTYkRidGKUYpNiRGJ0YnRik2JEYmRiZGJjYkRiZGJyIiITYkRidGJkYw QyQtSSVyYW5rRzYiNiNJI00yR0YlIiIi IiIj Pkkmc29sdWNHNiItSSZldmFsbUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLUkjJipHRiQ2JEkjTTJHRiQtJkknVmVjdG9yR0YnNiNJJ2NvbHVtbkdGJDYjL0kkJWlkR0YkIipnIXBNOg== PTYiNiM7IiIiIiIjRVxbbCNGJiwmJkkieEdGIzYjRiZGJiZGKzYjIiIkRi9GJywmJkYrNiNGJ0YvRi1GLw== QyUvJkkmc29sdWNHNiI2IyIiIiIiIUYoLyZGJTYjIiIjRik= LywmJkkieEc2IjYjIiIiRigmRiU2IyIiJEYrIiIh LywmJkkieEc2IjYjIiIjIiIkJkYlNiNGKUYpIiIh QyQ+SSJ4RzYiLUkpbGluc29sdmVHRiU2JEkiTUdGJUkiYkdGJSIiIg== PTYiNiM7IiIiIiIkRVxbbCRGJiwkJkkjX3RHRiM2I0YmISIkIiIjLCRGKiEiIkYnRio= JSFH Ecuaciones param\303\251tricas QygvLiZJInhHNiI2IyIiIkYlRikvLiZGJjYjIiIjRixGKS8uJkYmNiMiIiRGMUYp LyZJInhHNiI2IyIiIiwkJkkjX3RHRiVGJiEiJA== LyZJInhHNiI2IyIiIywkJkkjX3RHRiU2IyIiIiEiIg== LyZJInhHNiI2IyIiJCZJI190R0YlNiMiIiI= NiI= BKer(f)={(-3-1,1)} es una base del n\303\272cleo de f f no es inyectiva JSFH d) PkkidUc2IjcmIiIiISIiIiIkRig= NyYiIiIhIiIiIiRGJQ== QyQ+SSJ4RzYiLUkpbGluc29sdmVHRiU2JEkiTUdGJUkidUdGJSIiIg== PTYiNiM7IiIiIiIkRVxbbCRGJiwmRiZGJiZJI190R0YjNiNGJiEiJCIiIywmRiZGJkYqISIiRidGKg== JSFH e) Halla la matriz de la aplicaci\303\263n en las bases B'\342\204\2353={(1,4,1), (-5,3,2),(0,1,-3)} y B'\342\204\2354={(1,1,0,0),(1,0,-1,2),(2,0,0,3),(1,2,0,-1)} 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 LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKikpNCo0Og== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZGV0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEiUEYnRi9GMi9GM1Enbm9ybWFsRic= ISN3 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 LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKms7KW88 ISIi PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkISIiNiRGJ0YmISIkNiRGJkYmIiInNiRGJ0YnRio2JEYmRiohIiY2JEYqRioiIiE2JEYmRichIiU2JEYnRipGKzYkRidGK0YmNiRGKkYmRjU2JEYmRishIiM2JEYrRitGJjYkRitGKkYmNiRGKkYnRjU2JEYrRiZGLDYkRitGJ0Ym 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 PTYiNiQ7IiIiIiIlO0YmIiIkRVxbbC02JCIiI0YpIiM/NiRGJ0YmIiM+NiRGJkYmISNVNiRGJkYsISNqNiRGLEYsISIoNiRGJ0YsIiNKNiRGJ0YpIiNBNiRGLEYmISM4NiRGJkYpISNONiRGKUYpISIpNiRGKUYsRi02JEYpRiZGLQ== JSFH f) Halla la imagen del subespacio vectorial W cuyas ecuaci\303\263n cartesiana es z1+z2-5z3=0 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 PCUvSSN6MUc2IiwmSSN6MkdGJSEiIkkjejNHRiUiIiYvRidGJy9GKUYp Hallamos una base de W 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 NyUhIiIiIiIiIiE= NyUiIiYiIiEiIiI= Transformamos los vectores de la base de W 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 PTYiNiM7IiIiIiIlRVxbbCVGJiEiIiIiI0YmIiIkRilGJ0Yr 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 PTYiNiM7IiIiIiIlRVxbbCVGJiIiKSIiIyEiKSIiJCIjPEYnRiw= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= Calculamos las ecuaciones de f(W) con estos vectores porque son linealmente independientes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= g) Halla la imagen del subespacio vectorial W' cuya ecuaci\303\263n cartesiana es x1+3x3=0 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 PCQvSSN6MUc2IiwkSSN6M0dGJSEiJC9GJ0Yn Base de W' 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 NyUhIiQiIiEiIiI= NyUiIiEiIiJGIw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= Im\303\241genes de los vectores de la base de W' 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 PTYiNiM7IiIiIiIlRVxbbCVGJiIiISIiI0YpIiIkRiZGJ0Yr PTYiNiM7IiIiIiIlRVxbbCVGJiIiISIiI0YpIiIkRiZGJ0Yr LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkM= W' tiene dimensi\303\263n 1 y est\303\241 generado por el vector 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 JSFH JSFH JSFH JSFH JSFH JSFH JSFH Son linealmente dependientes TTdSMApJNlJUQUJMRV9TQVZFLzE1MzQ2NzU4OFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJSIkIiIiISIiIiIjIiIhRipGKkYnIiIkRishIiQiIihGK0YmTTdSMApJNlJUQUJMRV9TQVZFLzE1MzQ2ODkzMlgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIy0iJSIkIiIiRiciIiMiIiFGKUYpRiciIiQmJSJ6RzYjRicmRiw2I0YoJkYsNiNGKiZGLDYjIiIlRiY=