1. ## Indefinite matrix

hello to everybody !

could someone shed a light on this please.

the following matrix is given:

Code:
2, 5, 1, 0
5, 2, -2, 1
1, -2, 1, 0
0, 1, 0, 8
now, show that this matrix is indefinite by calculating (x^t)(Ax) with the vektors x^t = (1,1,0,0) and x^t=(0,1,1,0).

2. Originally Posted by vanilla1
hello to everybody !

could someone shed a light on this please.

the following matrix is given:

Code:
2, 5, 1, 0
5, 2, -2, 1
1, -2, 1, 0
0, 1, 0, 8
now, show that this matrix is indefinite by calculating (x^t)(Ax) with the vektors x^t = (1,1,0,0) and x^t=(0,1,1,0).
$x^tAx=(1\;1\;0\;0)\begin{pmatrix}2&5&1&0\\5&2&\!\! \!\!-2&1\\1&\!\!\!\!-2&1&0\\0&1&0&8\end{pmatrix}\left(\begin{array}{c}1 \\1\\0\\0\\\end{array}\right)$ $=14>0$ .
Now show that with the other vector you get a negative result and thus $A$ is indefinite.