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Practice n°5 - Linear Algebra

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Short test of two questions on COMPLEXIFICATION OF VECTOR SPACES AND LINEAR TRANSFORMATIONS. NORMAL FORMS OF NILPOTENT LINEAR TRANSFORMATIONS in Spanish

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Linear Algebra
Course
Linear algebra

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UNIVERSIDAD NACIONAL MAYOR DE SAN MARCOS
(Universidad del Perú, Decana de América)
Facultad de Ciencias Fı́sicas
Control N◦ 5 de Álgebra Lineal

1.(8p) Sea T ∈ L(IR3 ) definida por:

T (x, y, z) = (−x − 3y + 4z, −4x + 4z, 3x − 4y).

Determine si T es diagonalizable. Justifique.


2.(12p) Dada la transformación lineal T ∈ L(IR2 ) definida por:

T (x, y) = (−7x + 5y, −x − 3y)

Obtenga la representación matricial más simple asociada a T . Exhiba la base
que consigue dicha representación matricial.



Soledad Ramı́rez C.
Ciudad Universitaria, 7 de Setiembre de 2021




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April 7, 2022
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Written in
2021/2022
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Subjects

  • linear algebra
  • diagonalizable
  • linear transformation
  • matrix representation
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