Monthly Archives: March 2014

Linear Algebra and Its Applications, Exercise 3.1.11

Exercise 3.1.11. Fredholm’s alternative to the fundamental theorem of linear algebra states that for any matrix and vector either 1) has a solution or 2) has a solution, but not both. Show that assuming both (1) and (2) have solutions … Continue reading

Posted in linear algebra | Tagged , | Leave a comment

Linear Algebra and Its Applications, Exercise 3.1.10

Exercise 3.1.10. Given the two vectors and find a homogeneous system in three unknowns whose solutions are the linear combinations of the vectors. Answer: In the previous exercise 3.1.9 we showed that the plane spanned by the vectors and was … Continue reading

Posted in linear algebra | Tagged , , | Leave a comment

Linear Algebra and Its Applications, Exercise 3.1.9

Exercise 3.1.9. For the plane in spanned by the vectors and find the orthogonal complement (i.e., the line in perpendicular to the plane). Note that this can be done by solving the system where the two vectors are the rows … Continue reading

Posted in linear algebra | Tagged , , | Leave a comment