Linear Dependence in Rn with Nonsingular Matrix A

[aargoo]

Homework Statement

Let x₁,x₂,x₃ be linearly dependent vectors in Rⁿ, let A be a nonsingular n x n matrix, and let y₁=Ax₁, y₂=Ax₂, y₃=Ax₃. Prove that y₁, y₂,y₃ are linearly dependent.

Homework Equations

The Attempt at a Solution

My solution was y is equal to the zero vector, thus must be linearly dependent.

 

[Orodruin]

What is y in your solution? You have specified y1, y2, and y3 ...

 

[HallsofIvy]

I think you must have misunderstood the problem. y certainly does NOT have to be the 0 vector.

 

[Fredrik]

What does the assumption tell you about the vectors $x_1,x_2,x_3$? The answer to the problem follows almost immediately from the answer to this question.

 

[Quesadilla]

Without trying to derail the thread too much, I don't see why $A$ has to be nonsingular.