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Question Number 193554 by Mingma last updated on 16/Jun/23

Answered by aba last updated on 17/Jun/23

a=1 ∧ b=0

$$\mathrm{a}=\mathrm{1}\:\wedge\:\mathrm{b}=\mathrm{0}\: \\ $$

Answered by aba last updated on 17/Jun/23

 (((1   0)),((0   1)) )^k = (((1^k    0)),((0    1^k )) ) = (((1   0)),((0   1)) )   (((    a         b)),((−b        1)) )^6 =  (((1   0)),((0   1)) )^6 ⇒  (((    a      b)),((−b      1)) ) = (((1    0)),((0    1)) )  ⇒ { ((a=1 ✓)),((b=0 ✓)) :}

$$\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}^{\mathrm{k}} =\begin{pmatrix}{\mathrm{1}^{\mathrm{k}} \:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\mathrm{1}^{\mathrm{k}} }\end{pmatrix}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\:\:\:\:\mathrm{a}\:\:\:\:\:\:\:\:\:\mathrm{b}}\\{−\mathrm{b}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}^{\mathrm{6}} =\:\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}^{\mathrm{6}} \Rightarrow\:\begin{pmatrix}{\:\:\:\:\mathrm{a}\:\:\:\:\:\:\mathrm{b}}\\{−\mathrm{b}\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\Rightarrow\begin{cases}{\mathrm{a}=\mathrm{1}\:\checkmark}\\{\mathrm{b}=\mathrm{0}\:\checkmark}\end{cases} \\ $$

Commented by Rupesh123 last updated on 17/Jun/23

Perfect ��

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