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?
Hello, Oldspice1212!
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: .$\displaystyle 20 - 5h \:=\:0 \quad\Rightarrow\quad h \:=\:4$
$\displaystyle \text{The system is consistent for all }h \ne 4.$