\(\begin{array}{l}
A = \left[\matrix{2&-3\cr 4&7}\right];\quad B = \left[\matrix{2&4\cr -3&30\cr 30&1}\right];\quad C = \left[\matrix{-1&2&30\cr 1&5&1}\right]\\
a) \quad \begin{cases}a_{21}= 4\\ b_{32} = 1\\c_{22} = 5
\end{cases}\\
b)\quad M = A.C + B^{T}\\
\Leftrightarrow M = \left[\matrix{2&-3\cr 4&7}\right]\cdot\left[\matrix{-1&2&30\cr 1&5&1}\right] + \left[\matrix{2&-3&30\cr 4&30&1}\right]\\
\Leftrightarrow M = \left[\matrix{-5&-11&57\cr 3&43&127}\right] + \left[\matrix{2&-3&30\cr 4&30&1}\right]\\
\Leftrightarrow M = \left[\matrix{-3&-14&87\cr 7&73&128}\right]\\
c)\quad A = \left[\matrix{2&-3\cr 4&7}\right]\\
\xrightarrow{r_2 - 2r_1 \to r_2}\left[\matrix{2&-3\cr 0&13}\right]\\
\Rightarrow \det(A) = 2\\
+)\quad C.A = \varnothing\\
\text{Sửa đề: Tính}\ \det(C.B)\\
\quad C.B = \left[\matrix{-1&2&30\cr 1&5&1}\right]\cdot \left[\matrix{2&4\cr -3&30\cr 30&1}\right]\\
\Leftrightarrow C.B = \left[\matrix{892&87\cr 17&154}\right]\\
\xrightarrow{r_2 - \tfrac{17}{892}r_1 \to r_2} \left[\matrix{892&87\cr 0&\dfrac{135889}{892}}\right]\\
\Rightarrow \det(C.B) = 2
\end{array}\)
