The matrix $\left[ {\begin{array}{*{20}{c}}2&5&{ – 7}\\0&3&{11}\\0&0&9\end{array}} \right]$is known as

A trust fund has Rs. $30,000$ that must be invested in two different types of bonds. The first bond pays $5 \%$ interest per year, and the second bond pays $7 \%$ interest per year. Using matrix multiplication, determine how to divide Rs. $30,000$ among the two types of bonds. If the trust fund must obtain an annual total interest of  Rs.  $1800$.

If $\quad A=\left[\begin{array}{cc}\cos \theta & \text { isin } \theta \\ \operatorname{isin} \theta & \cos \theta\end{array}\right], \left(\theta=\frac{\pi}{24}\right)$ and $A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],$ where $i=\sqrt{-1},$ then which one of the following is not true?

Let $P = \left[ {\begin{array}{*{20}{c}}
  1&0&0 \\ 
  3&1&0 \\ 
  9&3&1 
\end{array}} \right]$ and $Q = [q_{ij}]$ be two $3\times3$ matrices such that $Q -P^5 = I_3$. Then $\frac{{{q_{21}} + {q_{31}}}}{{{q_{32}}}}$ is equal to

If $A = \left[ {\begin{array}{*{20}{c}}1&0&1\\0&1&1\\1&0&0\end{array}} \right]$, then $A$ is