written 3.0 years ago by | modified 2.2 years ago by |
Find non-Singular Matrices P & Q such that, $A=\begin{bmatrix}1 & 2 & 3 & 4\\2 & 1 & 4 & 3\\3 & 0 & 5 & -10 \end{bmatrix} $
is reduced to normal form. Also find rank.
written 3.0 years ago by | modified 2.2 years ago by |
Find non-Singular Matrices P & Q such that, $A=\begin{bmatrix}1 & 2 & 3 & 4\\2 & 1 & 4 & 3\\3 & 0 & 5 & -10 \end{bmatrix} $
is reduced to normal form. Also find rank.
written 3.0 years ago by | modified 2.7 years ago by |
$A=\begin{bmatrix}1&2&3&4\\ 2&1&4&3\\ 3&0&5&-10\end{bmatrix} $
$Let\ A=I_3AI_4\\$ \begin{bmatrix}1&2&3&4\\ 2&1&4&3\\ 3&0&5&-10\end{bmatrix}=\begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix} A \begin{bmatrix}1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1\end{bmatrix} $$
$By\ R_2-2R_1, R_3-2R_1\\ \begin{bmatrix}1&2&3&4\\ 0&-3&-2&-5\\ 0&-6&-4&-22\end{bmatrix} =\begin{bmatrix}1&0&0\\ -2&1&0\\ -3&0&1\end{bmatrix} A \begin{bmatrix}1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1\end{bmatrix} $
$$By \ C_2-2C_1, C_3-3C_1 , C_4-4C_1 \ \begin{bmatrix}1&0&0&0\ 0&-3&-2&-5\ 0&-6&-4&-22\end{bmatrix} =\begin{bmatrix}1&0&0\ -2&1&0\ -3&0&1\end{bmatrix} A \begin{bmatrix}1&-2&-3&-4\ 0&1&0&0\ 0&0&1&0\ 0&0&0&1\end{bmatrix} …