
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Exercises on linear algebra, focusing on finding the kernel of a linear transformation t, determining linear independence, finding a basis and calculating the dimension of a subspace. The exercises involve finding the matrix representation of a linear transformation and applying it to vectors, as well as determining if given matrices form a linearly independent set and finding a basis for the span of those matrices.
Typology: Assignments
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Complete the following exercises.
a b c d
c − 2 a 2 b 0 a − d + c
(a) Is S a linearly independent set? (b) Find a basis B for span(S). (c) What is the dimension of span(S)?
(d) Write the matrix A =
as a linear combination of the vectors in the basis B. (e) What is the coordinate vector [A]B? (f) For what value of k is [A]B ∈ Rk? (g) Let C be the standard basis of M 2 × 2. For what value of k is [A]C ∈ Rk? What is [A]C?
(a) Find a basis for V. (b) What is the dimension of V?