Question

In modern control system, d matrix is called as

a.observation matrix

b.transmission matrix

c.control matrix

d.system matrix

Answer 1

d option is correct.
system matrix

Answer 2

Explanation:

$\sf A = \left[ \begin {array}{cc} 2 & 4 \\ 1 & 1 \end {array} \right]$

$\sf {A}^{2} - 3A - 2I = 0$

$\sf Multiplying \: with \: {A}^{-1}$

$\sf {A}^{2}{A}^{-1} - 3A {A}^{-1} - 2I {A}^{-1} = 0$

$\sf We \:know\:that \: A {A}^{-1} = I$

$\sf AI - 3I - 2I{A}^{-1} = 0$

$\sf \left [ \begin {array}{cc} 3 & 4 \\ 1 & 1 \end {array} \right] - \left [ \begin {array}{cc} 3& 0\\ 0& 3 \end {array} \right] = 2I {A}^{-1}$

$\sf \left [ \begin{array}{cc} 3 - 3 & 4 -0 \\ 1 - 0 & 1 - 3 \end {array} \right] = 2 {A}^{-1}$

$\sf \left [ \begin {array}{cc} 0& 4\\ 1& - 2 \end {array} \right] = 2 {A}^{-1}$

$\sf {A}^{-1} = \left [ \begin {array}{cc} 0& 2\\ \frac {1}{2}& - 1 \end {array} \right]$

#Puhkar