Find the inverse of each of the matrices (if it exists) given in $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

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Find the inverse of each of the matrices (if it exists) given in $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

$\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

Solution:

Let $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

\text { (1) }

$|A|=\left|\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right|=1(10)-2(0)+3(0)=10 \neq 0$

Therefore,
$A^{-1}$ exists

A₁₁ = , A₁₂ = ,

A₁₃ = , A₂₁ = ,

A₂₂ = , A₂₃ = ,

A₃₁ = , A₃₂ = ,

A₃₃ =

adj. A =

i

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