Q4 Verify Cayley-Hamilton theorem for the given matrix. \[ A=\left[\begin{array}{ccc}1 & 2 & -1 \\ 2 & 1 & -2 \\ 2 & -2 & 1\end{array}\right] \] Find, also, \( A^{4} \) using Cayley-Hamilton theorem.

You deposit \( \$ 300 \) each month into an account earning \( 3 \% \) interest compounded monthly. a) How much will you have in the account in 30 years? b) How much total money will you put into the account? \( \$ \) c) How much total interest will you earn? \( \$ \) \$

Determine \( \lim _{x-{ }_{-3}} \frac{x^{2}-x-12}{x+3} \)

In \( \triangle X Y 2 \) and \( \triangle L M N, \angle X=\angle M \) and \( \angle 4=\angle M \) which sicle of \( \triangle \angle M M \) Should be equal to the Sicle \( X Y \) of \( \triangle X Y 2 \) So that the two triang are congrient? Give keoson?

Factor. \( 64 x^{3}-729 y^{3} \)

EJERCICIOS PROPUESTOS (1) \( 3 x+2(x-2)=5 x-4 \) (2) \( -2(1-2 x)-(1-2 x)=-x-2 \) (3) \( 2 x+4=3 x+3(x-2)-4 \) (4) \( 5(2 x-2)-4 x=-3(2-x) \) (5) \( 50-[3(2 x-3)-2(2 x-1)]=23 \) (6) \( 8 x+(-5 x-9)=3 x+[-5 x-(x+3)] \) (7) \( 71+[-(3 x+4)-(4 x+3)]=25-[-5 x+(-2 x+3)] \) (8) \( \frac{3 x+1}{3}=\frac{x-3}{6}+\frac{5}{12} \) (9) \( \frac{3 x+1}{8}-\frac{x-1}{6}=\frac{x+3}{4} \) (10) \( \frac{5-x}{4}-\frac{x+3}{6}=\frac{9-x}{4}-\frac{6 x-2}{16} \)