Linear algebra

[Ryan Rigdon]

Here is my question. Any ideas on how i may start it?

Suppose A is mxn and b is in R^m. What has to be true about the two numbers rank [ A b ] and rank A in order for the equation Ax=b to be consistent?

I think i have an idea.

"For the equation Ax=b to be consistent, the rank [A b] must equal the rank A."

i just feel something is missing.

 

[daon2]

Here is my question. Any ideas on how i may start it?

Suppose A is mxn and b is in R^m. What has to be true about the two numbers rank [ A b ] and rank A in order for the equation Ax=b to be consistent?

I think i have an idea.

"For the equation Ax=b to be consistent, the rank [A b] must equal the rank A."

i just feel something is missing.

What do you mean by [ A b ]? The matrix formed by augmenting the columns of A with b? If so, I agree with you. Ax=b is consistent iff b is already in the column space of A.

 

[Ryan Rigdon]

thats the way it was set up. [ A b ]

 

[HallsofIvy]

thats the way it was set up. [ A b ]

Yes, now answer the question- what does that mean? If you don't know what the notation means, how can you hope to answer the question?