# Linear Dependence Proof

1. Jul 30, 2014

### aargoo

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
My solution was y is equal to the zero vector, thus must be linearly dependent.

2. Jul 30, 2014

### Orodruin

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

3. Jul 31, 2014

### HallsofIvy

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

4. Jul 31, 2014

### Fredrik

Staff Emeritus
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.

5. Jul 31, 2014

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