Went ahead and did the HW the teach recommended but she did not post the answers and I would like to see if im on the right track.
Problem 1: Are the vectors (2,−1,−3), (3, 0,−2), (1, 1,−4) linearly independent?
Problem 2 : Is the set {x E R^4 : (x1 − x2)^2 + x3^4 = 0} a subspace? Justify
Problem 3 : Solve the system
2x1 + x2 + 3x3 + x4 = 1
x2 + 4x3 + x4 = 1
3x1 + 2x4 = 1.
Problem 4 : Find an othonormal basis of the subspace S = {x E R^4 :
x1 + x2 + x3 + x4 = x1 − x2 − 2x3 + x4 = x2 + 3x3 = 0}. What is the dimension on S?
Problem 5 : Let
A = 0 2 −1
1 2 3
2 2 −1
Compute A−1.
Problem 6: Find the eigenvalues and eigenvectors of
A = −1 1
1 −2
Problem 7: Find the eigenvalues and eigenvectors of
A = −2 1
−4 −2