Question Number 113504 by Khalmohmmad last updated on 13/Sep/20
Commented by Khalmohmmad last updated on 13/Sep/20
$$\mathrm{Please}\:\mathrm{Solve} \\ $$
Commented by kaivan.ahmadi last updated on 13/Sep/20
![A^2 = [((1 2)),((0 1)) ] A^3 = [((1 3)),((0 1)) ] ⋮ A^(27) = [((1 27)),((0 1)) ]⇒a+b+c+d=29](https://www.tinkutara.com/question/Q113541.png)
$${A}^{\mathrm{2}} =\begin{bmatrix}{\mathrm{1}\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\mathrm{1}}\end{bmatrix} \\ $$$${A}^{\mathrm{3}} =\begin{bmatrix}{\mathrm{1}\:\:\:\:\mathrm{3}}\\{\mathrm{0}\:\:\:\:\:\mathrm{1}}\end{bmatrix} \\ $$$$\vdots \\ $$$${A}^{\mathrm{27}} =\begin{bmatrix}{\mathrm{1}\:\:\:\mathrm{27}}\\{\mathrm{0}\:\:\:\:\:\:\mathrm{1}}\end{bmatrix}\Rightarrow{a}+{b}+{c}+{d}=\mathrm{29} \\ $$
Commented by bobhans last updated on 13/Sep/20
$$\mathrm{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{k}}\\{\mathrm{0}\:\:\:\:\:\mathrm{1}}\end{pmatrix}\:\Rightarrow\:\mathrm{A}^{\mathrm{n}} \:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{nk}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$