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(a) Consıder the followng system of equations
$$\left\{\begin{array}{r} x_{1}-3 x_{2}=2 \\ 2 x_{2}=6 \end{array}\right.$$
(i) write down the coefficient matrix of the above system
(n) using back substitution, solve the above system
(b) Let
$$A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right] \quad, B=\left[\begin{array}{rr} 2 & 1 \\ -3 & 2 \end{array}\right], C=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right]$$
and determme as to whether or not
(1) $A(B C)=(A B) C$
(11) $A(B+C)=A B+A C$
(c) Let $D, E$ be nonsmgular matrices and show that $(D E)^{-1}=E^{-1} D^{-1}$
(d) Compute the inverse of the following matrix
$$F=\left[\begin{array}{rr} -1 & 1 \\ 1 & 0 \end{array}\right]$$
and verify that $t$ 4
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