# Homework Help: Singular matrices

1. Feb 2, 2010

### EV33

1. The problem statement, all variables and given/known data
Let A = [A1,...,An-1] be an (nx(n-1)) matrix. Show that B = [A1,...,An-1,Ab] is singular for every choice of b in R^n-1.

2. Relevant equations
Ax = 0

3. The attempt at a solution
I know that if B is singular that means that for the equation Bx = 0 there exists another solution another than the trivial solution (x = 0). Now if we made B have all the same columns as A except added a new column Ab, that would make B a square matrix that is (nxn). But from there, I can't figure out how to use the information I know to solve the problem...

2. Feb 2, 2010

If a matrix is singular, then its columns are linearly dependent. Any ideas?

3. Feb 2, 2010

### Matthollyw00d

Ab=[A1b A2b ... An-1b]^T so by construction the column Ab is a linear combination of the first n-1 column vectors, regardless of what the vector b actually is. Hence detB=0

4. Feb 2, 2010

### EV33

radou isn't that only true if the matrix is two by two?

And Matthollywood I am not sure what you are saying, could you please reword what you said.

Thank you.