Construct matrix A where Ax=b has a solution but Ax=c does not

[Jen2114]

Homework Statement

Construct a 3x3 matrix A and vectors b and c in R^3 so that Ax=b has a solution but Ax=c

Homework Equations

The Attempt at a Solution

So I don't know where to start. I am not sure if the problem is asking me to create a matrix with real numbers or variables. What I do know is that Ax=b has a solution if each row has a pivot , except the last column. So How would I use this to answer the question?

 

[andrewkirk]

You left off a "doesn't" at the end of the question.

Taking that as read, the matrix has to be singular, otherwise we can just left-multiply both sides by $A^{-1}$ to find solutions for both equations.

What is the simplest, most monotonous, singular, 3 x 3 matrix you can think of?

If you call that matrix A, what is the only vector b for which A x = b will have a solution x?

I suspect that may not be the matrix they are looking for, but that's the simplest and most natural answer to the question as posed.

 

[Jen2114]

Ok thank you for your help