Solving Line Space Problem with Matrices A & B

[Cyannaca]

Consider the matrices

A=
(1 5 -3)
(2 x -3)

B=
(1 3 -1)
(3 x -1)

Find x so A and B have the same line space.
I tried to do this problem but I was stuck with

A=
(1 (x-5) 0)
(0 (x-10) 3)

B=
(1 3 -1)
(0 (x-9) 2)

Also, I'm not really sure of what they mean by same line space.

 

[matt grime]

If you don't know what the definition of "line space" is from your notes, then we're not guaranteed to know. Indeed the only definition I could find was that it was a Liouville space, which is a product of Hilbert spaces, so I don't think that's waht you want.

 

[Data]

Is it possible they mean "row" space? Or "column" space (unlikely, since they have the same column space in $\mathbb{R}^2$ regardless of the value of x)? Ask your intructor.

 

[Cyannaca]

Yes, they mean row space. Sorry, I translated it from French a bit too fast I guess. Actually, I have to find the value of x so they have the same row space but I don't know how.

 

[matt grime]

Row reduce into ecehlon form, the resulting vectors must have the same spane. Finding the span is the same as finding solutions to simultaneous equations. If you use reduced row echelon form the answer is even easier to read off. These topics will almost certainly bi in your notes, though I don't know the French terms for them (though I can guess what echelon is).