Embibe Experts Solutions for Exercise 3: Assignment

If $A=\left[\begin{array}{ll}3& 2\\ 4& 5\end{array}\right].$ Find $A^2$

If $A=\left[\begin{array}{ll}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{rr}1& 3\\ -2& 5\end{array}\right],C=\left[\begin{array}{rr}-2& 5\\ 3& 4\end{array}\right]$ . Find the following
(i) $3A-C$
(ii) $2A-B-3C$

If $A=\left[\begin{array}{lll}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$, verify that $A^2=I$.

A trust fund has $₹$90,000 that must be invested in two different types of bonds. The first type of bond pays $10\%$ interest per year and the second type pays $12\%$. Using matrix multiplication, determine how to invest $₹$ $90000$ into two types of bonds so that the total annual interest received is Rs 9600.

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ x& 2& y\end{array}\right]$ is a matrix satisfying $A{A}^{\text{'}}=9I_3$. Find values of $x$ and $y$

Using elementary row transformations, find inverse of $A=\left[\begin{array}{lll} 2& -1& 3\\ -5& 3& 1\\ -3& 2& 3\end{array}\right]$

If $A=\left[\begin{array}{cc}\cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{array}\right]$ and $i=\sqrt{-1}$ then prove by induction that $A^n=\left[\begin{array}{cc}\cos n\theta & i\sin n\theta \\ i\sin n\theta & \cos n\theta \end{array}\right],n\in N$

By using elementary row transformation, find $A^{-1}$, where $A=\left[\begin{array}{ccc}4& -6& 6\\ 4& 4& 6\\ 6& -4& 4\end{array}\right]$.