Infinitely Solvable Matrix: When the Bottom Row is 0,0,1,1

[Nope]

Homework Statement

the system have infinitely solutions when the bottom row is 0,0,0,0, what If the bottom row of the matrix is 0,0,1,1
like
X,Y,Z,
1,0,2,3
0,1,2,3
0,0,1,1
can i still say
the system have infinitly solution?

Homework Equations

The Attempt at a Solution

 

[fzero]

No, this system doesn't have infinitely many solutions. You can subtract multiples of the 3rd row from the 1st and 2nd rows to find the solution.

 

[silvermane]

Homework Statement

the system have infinitely solutions when the bottom row is 0,0,0,0, what If the bottom row of the matrix is 0,0,1,1
like
X,Y,Z,
1,0,2,3
0,1,2,3
0,0,1,1
can i still say
the system have infinitly solution?

Well, how many unknowns will you be left with in comparison to how many equations you have?
If the number of unknowns > number of equations, there's infinite solutions since you'll have a free variable.

 

[Nope]

Yea, I mean if you can't subtract or do anything on the bottom row, 0,0,1,1
so X3=X3,
is it infinite solutions?

 

[fzero]

Yea, I mean if you can't subtract or do anything on the bottom row, 0,0,1,1
so X3=X3,
is it infinite solutions?

You might want to explain what the matrix you wrote down means. The way I understand it, the last line is solved by x₃ = 1.

 

[Nope]

thx for replying
the matrix ...I just make it up,
sorry, it a bad example
I was trying to show an example of the bottom row is 0,0,1,1.
My main question is that
if i can't perform any row operation on the bottom row, 0,0,1,1
so X3=X3,
is it infinite solutions?
or there's no such matrix exist?

 

[fzero]

Can you write down what you think the matrix means? The way I understand it, it represents the set of equations

x_1 + 2 x_3 =3,
x_2 + 2 x_3 = 3,
x_3 = 1.

If it means something else, please explain.

 

[Nope]

it was suppose to be in the form x+y+z=any number
1,0,2,3
x+2z=3
just forget the matrix I wrote

 

[Nope]

Nevermind, I just figure it out... sorry, i was just confused on something