Consider the matrix
then,
Now, use Rouche-Fröbenius theorem.
Fernando Revilla
I'm doing a practice test for my Matrix Algebra exam. One of the questions says to "Use determinants to decide if the set of four vectors shown below is linearly dependent. Explain your reasoning."
(Sorry, not sure how to type out matrices. These are all 4x1 matrices)
v1 = [3]
.......[5]
.......[2]
.......[0]
v2= [0]
......[0]
......[1]
......[1]
v3 = [0]
.......[-2]
.......[-3]
.......[1]
v4 = [3]
.......[3]
.......[0]
.......[2]
I know how to determine linear dependence/independence, but not by using determinants. I can't find any examples in the notes.
I'm thinking I'd put them all in an augmented matrix and find the determinant of that, but how would I tell if it is linearly dependent?
Consider the matrix
then,
Now, use Rouche-Fröbenius theorem.
Fernando Revilla
No, it is linearly independent. If then, is an invertible matrix, so:
Fernando Revilla
All right, if then, the family is linearly dependent.
Fernando Revilla