Linear Independence of a 3x3 matrix

[bwilliams1188]

Homework Statement

A is a 3x3 matrix with distinct eigenvalues lambda(1), lambda(2), lambda(3) and corresponding eigenvectors u1,u2, u3.

Suppose you already know that {u1, u2} is linearly independent.

Prove that {u1, u2, u3} is linearly independent.

Homework Equations

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The Attempt at a Solution

I am supposed to prove that {u1, u2, u3} is linearly independent, but since there are distinct eigenvalues/vectors, is that not enough to say that {u1, u2, u3} is linearly independent?

 

[Mark44]

Homework Statement

A is a 3x3 matrix with distinct eigenvalues lambda(1), lambda(2), lambda(3) and corresponding eigenvectors u1,u2, u3.

Suppose you already know that {u1, u2} is linearly independent.

Prove that {u1, u2, u3} is linearly independent.

Homework Equations

??

The Attempt at a Solution

I am supposed to prove that {u1, u2, u3} is linearly independent, but since there are distinct eigenvalues/vectors, is that not enough to say that {u1, u2, u3} is linearly independent?

No, that's not enough. That's exactly what you need to prove.