csat-suneung· South-Korea· csat__math-science4 marks
Let the set $U$ be $$U = \left\{ \left. \left( \begin{array} { l l }
a & b \\
c & d
\end{array} \right) \right\rvert \, a , b , c , d \text{ are positive numbers not equal to } 1 \right\}$$ Let the subset $S$ of $U$ be $$S = \left\{ \left. \left( \begin{array} { l l }
a & b \\
c & d
\end{array} \right) \right\rvert \, \log _ { a } d = \log _ { b } c , \quad a \neq b , \quad b c \neq 1 \right\}$$ Which of the following are correct? Select all that apply from . [4 points] ㄱ. If $A = \left( \begin{array} { c c } 4 & 9 \\ 3 & 2 \end{array} \right)$, then $A \in S$. ㄴ. If $A \in U$ and $A$ has an inverse matrix, then $A \in S$. ㄷ. If $A \in S$, then $A$ has an inverse matrix. (1) ㄱ (2) ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
Let the set $U$ be
$$U = \left\{ \left. \left( \begin{array} { l l }
a & b \\
c & d
\end{array} \right) \right\rvert \, a , b , c , d \text{ are positive numbers not equal to } 1 \right\}$$
Let the subset $S$ of $U$ be
$$S = \left\{ \left. \left( \begin{array} { l l }
a & b \\
c & d
\end{array} \right) \right\rvert \, \log _ { a } d = \log _ { b } c , \quad a \neq b , \quad b c \neq 1 \right\}$$
Which of the following are correct? Select all that apply from <Remarks>. [4 points]
<Remarks>\\
ㄱ. If $A = \left( \begin{array} { c c } 4 & 9 \\ 3 & 2 \end{array} \right)$, then $A \in S$.\\
ㄴ. If $A \in U$ and $A$ has an inverse matrix, then $A \in S$.\\
ㄷ. If $A \in S$, then $A$ has an inverse matrix.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ