Question

Find the? inverse, if it? exists, for the given matrix.

[4 3]

[3 6]

Answer 1

Therefore, the inverse of given matrix is

`=\begin{pmatrix}(2)/(5)&-(1)/(5)\\ -(1)/(5)&(4)/(15)\end{pmatrix}`

Explanation:

The inverse of a square matrix
`A` is
`A^(-1)` such that

`A A^(-1)=I` where I is the identity matrix.

Consider,
`A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]`

`\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}`

`\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\\e 0`

`=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}`

`\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc`

`4\cdot \:6-3\cdot \:3=15`

`=(1)/(15)\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}`

`=\begin{pmatrix}(2)/(5)&-(1)/(5)\\ -(1)/(5)&(4)/(15)\end{pmatrix}`

Therefore, the inverse of given matrix is

`=\begin{pmatrix}(2)/(5)&-(1)/(5)\\ -(1)/(5)&(4)/(15)\end{pmatrix}`