# Linear algebra conceptual question

1. Jan 19, 2013

### Mdhiggenz

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

Let A be a 5x3 matrix. If

b=a1+a2=a2+a3

then what can you conclude about the number of solutions of the linear system Ax=b? Explain

I don't have the solution for this problem, and my first thinking was the system would be overdertermined, and be most likely inconsistent. However i'm not 100% if i am even approaching the problem correctly

Thanks

2. Relevant equations

3. The attempt at a solution

2. Jan 19, 2013

### Ray Vickson

What are $a_1, a_3, a_3$? Rows of A? Columns of A? Something else?

3. Jan 19, 2013

### Mdhiggenz

rows of a

4. Jan 19, 2013

### vela

Staff Emeritus
The rows of A have 3 elements each while b has 5 elements. How can $a_1+a_2=b$ possibly hold?

5. Jan 19, 2013

### Mdhiggenz

Don't really understand

6. Jan 19, 2013

### vela

Staff Emeritus
Look at the dimensions of A, x, and b. A is 5x3, so what do the dimensions of x and b have to be?

7. Jan 20, 2013

### Mdhiggenz

it would have to be 5x1?

8. Jan 20, 2013

### vela

Staff Emeritus
Right. Now if $a_1$ and $a_2$ represent rows of A, how many elements does each have? Can $a_1+a_2$ equal $b$?

9. Jan 20, 2013

### Mdhiggenz

5 elements in order to equal b.

and no a1+a2 alone can not equal b. it must be coupled with 4 other rows of a1+a2. I hope I interpreted that correctly.

10. Jan 20, 2013

### SammyS

Staff Emeritus
I suspect that a1, a2, and a3 are the columns of matrix A .

11. Jan 20, 2013

### Mdhiggenz

I think you're correct sammy I just reread the question.

12. Jan 20, 2013

### SammyS

Staff Emeritus
Can you get a solution now ?

13. Jan 20, 2013

### Mdhiggenz

Sorry but i'm still confused, I am having a hard time transitioning to this deeper thinking math course.

But I think the answer would be that a 5x3 matrix should have an answer in the 5x1 form

So b would be could be an infinite array of 5x1 different matrices.