CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$A=|a_{ij}|_{2\times 2}$$, where $$a_{ij}=\left\{\begin{matrix} i+j, & if & i\neq j\\ i^2-2j, & if & i=j\end{matrix}\right.$$, then $$A^{-1}=?$$


A
19[0331]
loader
B
19[0331]
loader
C
19[4112]
loader
D
19[4112]
loader

Solution

The correct option is A $$\dfrac{1}{9}\begin{bmatrix} 0 & 3\\ 3 & 1\end{bmatrix}$$
$$\begin{array}{l} A={ \left| { aij } \right| _{ 2\times 2 } } \\ { a_{ 11 } }=1-2=-1 \\ { a_{ 12 } }=3 \\ { a_{ 21 } }=3 \\ { a_{ 22 } }=4-2\times 2=0 \\ A=\left[ \begin{array}{l} -1 & 3 \\ 3 & D \end{array} \right]  \\ { A^{ -1 } }=\frac { 1 }{ { \left| A \right|  } } adjA \\ =\frac { { -1 } }{ { 09 } } \left[ \begin{array}{l} 0 & -3 \\ -3 & -1 \end{array} \right]  \\ =\frac { 1 }{ 9 } \left[ \begin{array}{l} 0 & 3 \\ 3 & 1 \end{array} \right]  \end{array}$$

Applied Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image