I2.1 If $\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|=a d-b c$ and $\left|\begin{array}{ll}3 & 4 \\ 2 & k\end{array}\right|=k$, find $k$.
I2.2 If $50 m=54^{2}-k^{2}$, find $m$.
$\mathbf{I 2 . 3}$ If $(m+6)^{a}=2^{12}$, find $a$.
I2.4 $A, B$ and $C$ are the points $(a, 5),(2,3)$ and $(4, b)$ respectively. If $A B \perp B C$, find $b$.
$\begin{array}{l}3 k-8=k \\ \Rightarrow k=4 \\ 50 m=54^{2}-4^{2}=(54+4)(54-4)=58 \times 50 \\ \Rightarrow m=58 \\ (58+6)^{a}=2^{12} \\ \Rightarrow 64^{a}=2^{12} \\ \Rightarrow 2^{6 a}=2^{12} \\ \Rightarrow a=2 \\ A(2,5), B(2,3), C(4, b) \\ A B \text { is parallel to } y \text {-axis } \\ \Rightarrow B C \text { is parallel to } x \text {-axis } \\ \Rightarrow b=3\end{array}$