Find the value of non singular matrices P and Q, such that PAQ is in the normal form, where A is \(\begin{bmatrix}1&1&2\
Posted: Thu Jul 14, 2022 9:41 am
a) \(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\)
b)\(\begin{bmatrix}1&1&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\)
c)\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&1\\0&1&-1\\0&0&1\end{bmatrix}\)
d)\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&0&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&-1\end{bmatrix}\)
b)\(\begin{bmatrix}1&1&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&1\end{bmatrix}\)
c)\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&1&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&1\\0&1&-1\\0&0&1\end{bmatrix}\)
d)\(\begin{bmatrix}1&0&0\\-1&1&0\\-1&0&1\end{bmatrix}\), \(\begin{bmatrix}1&-1&-1\\0&1&-1\\0&0&-1\end{bmatrix}\)