Math Is Fun Forum

EPhillips1989

Member

Registered: 2007-11-03

Posts: 29

matrices

X+Y+Z=1
(a+1)X+Y+(a^2+a)Z=1
(a-2)X+(a-2)Y-aZ=b
can anyone find solutions of this system of linear equations
for which values of a,b the system has
1) a unique solution
2)no solutions
3)infinitely many solutions

any help with this will be much appreciated!!!

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: matrices

How come I can't display matrices in LaTeX?

[math]\begin{bmatrix} 1 & 1 & 1 \\ a+1 & 1 & a^2+a \\ a-2 & a-2 & a \end{bmatrix}[/*math]

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: matrices

You can, but the code is different. Dross put a section about arrays in his superb LaTeX tutorial, stickied in this board.

Your system of equations looks like this in matrix form:

Now you use row operations to get that matrix into row-reduced echelon form, which will allow you to see how many solutions there are (I think).

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: matrices

The is the same matrix as the one MathsyPerson generated, but with a briefer code (using only one array).

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: matrices

Aha, nice trick. Thanks.

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Why did the vector cross the road?
It wanted to be normal.

EPhillips1989

Member

Registered: 2007-11-03

Posts: 29

Re: matrices

is this now in reduced echelon form???

1  1  1            1
0  a  (a^2-3)  -2
0  0   2           (b-a+2)