Find the inverse of the following matrices (i)\left[\begin{array}{rr}2 & 5 \\ -3 & 1\end{array}\right]
Sol : A=\left[\begin{array}{ll}2 & 5 \\ -3 & 1\end{array}\right]
(ii)\left[\begin{array}{rr}2 & -2 \\ 1 & 3\end{array}\right]
Sol :
(iii)\left[\begin{array}{rr}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right] where a^{2}+b^{2}+c^{2}+d^{2}=1
Sol : A=\left[\begin{array}{rr}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right]
|A|=(a+ib)(a-ib)-(-c+id)(c+id)
=a^{2}-1^{2} b^{2}+c^{2}-i^{2} d^{2}
=a^{2}+b^{2}+c^{2}+d^{2}
=1≠0
<to be added>
A_{11}=a-i b , A_{12}=-(-c+i d)=c-id
A_{21}=-(c+i d)
=-c-id
A_{22}=a+ib
ad{j} A=\left[\begin{array}{cc}a-ib & c-i d \\ -c-i d & a+i b\end{array}\right]
=\left[\begin{array}{cc}a-i b & -c-i d \\ c-i d & a+i b\end{array}\right]
A^{-1}=\frac{1}{(A)} \cdot a d j A
=\frac{1}{1}\left[\begin{array}{cc}a-i b & -c-i d \\ c-i d & a+2 b\end{array}\right]
A^{-1}=\left[\begin{array}{cc}a-i b & -c-i d \\ c-i d & a+i b\end{array}\right]
(iv) \left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right] Sol :
(v) \left[\begin{array}{ll}a & b \\ c & d\end{array}\right]. जहाँ (where) ad-bc≠0 Sol :
Question no 9 ka 3 sol
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