# h such that the matrix is augmented...

• Jan 22nd 2013, 02:55 PM
Oldspice1212
h such that the matrix is augmented...
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system?

1 h 2
5 20 8

Ok so I got 2h cannot = - 20
Then divide by 2 and got h cannot equal = -10?

Is this correct?
• Jan 22nd 2013, 03:10 PM
Plato
Re: h such that the matrix is augmented...
Quote:

Originally Posted by Oldspice1212
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system?

1 h 2
5 20 8

Ok so I got 2h cannot = - 20
Then divide by 2 and got h cannot equal = -10?
Is this correct?

No it is not correct.

You need the matrix $\displaystyle \left[ {\begin{array}{*{20}c} 1 & h \\ 5 & {20} \\ \end{array} } \right]$ to be non-singular, determinate not zero.
• Jan 22nd 2013, 03:21 PM
Oldspice1212
Re: h such that the matrix is augmented...
I have to make it into a

1 0
0 1

Is that what you mean?
• Jan 22nd 2013, 03:32 PM
Plato
Re: h such that the matrix is augmented...
Quote:

Originally Posted by Oldspice1212
I have to make it into a

1 0
0 1

Is that what you mean?

No you must have $\displaystyle (1)(20)-(5)(h)\ne 0~.$
• Jan 22nd 2013, 03:34 PM
Oldspice1212
Re: h such that the matrix is augmented...
Ooh haha I got -4, does it look correct now?
• Jan 22nd 2013, 03:38 PM
Plato
Re: h such that the matrix is augmented...
Quote:

Originally Posted by Oldspice1212
Ooh haha I got -4, does it look correct now?

No that is not correct.
And I think that you are just guessing.
Read the question. If you understand the process, then the answer is easy.
• Jan 22nd 2013, 03:54 PM
Oldspice1212
Re: h such that the matrix is augmented...
Its 4 since (20-5h)x2=-2
So it's a augmented matrix of a consistant linear system if h cannot = 4? :D
• Jan 22nd 2013, 04:07 PM
Soroban
Re: h such that the matrix is augmented...
Hello, Oldspice1212!

Quote:

Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.

. . $\displaystyle \left[\begin{array}{cc|c} 1&h&2 \\ 5&20&8 \end{array}\right]$

The system is consistent if its determinant is not equal to zero.

If $\displaystyle D = 0$, we have: .$\displaystyle \begin{vmatrix}1&h \\ 5&20\end{vmatrix} \:=\:0$

. . Hence: .$\displaystyle 20 - 5h \:=\:0 \quad\Rightarrow\quad h \:=\:4$

$\displaystyle \text{The system is consistent for all }h \ne 4.$
• Jan 22nd 2013, 04:09 PM
Oldspice1212
Re: h such that the matrix is augmented...
^ yup I got it, thanks guys :D