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2.(a) (i) Use row operations to find the inverse of (ii) Using the inverse matrix found above, solve the equation AX = B where (b) Use properties of determinants to

(i) Factorise A=\left[\begin{array}{ccc} 1 & -1 & 2 \\ 3 & 2 & 4 \\ 0 & 1 & -2 \end{array}\right] B=\left[\begin{array}{l} 3 \\ 6 \\ 1 \end{array}\right] \left|\begin{array}{ccc} z^{2} & y^{2} & x^{2} \\ z & y & x \\ 3 & 3 & 3 \end{array}\right| \left|\begin{array}{ccc} 1 & b c & b c(b+c) \\ 1 & c a & c a(c+a) \\ 1 & a b & a b(a+b) \end{array}\right|=a b c\left|\begin{array}{lcc} a & 1 & b+c \\ b & 1 & c+a \\ c & 1 & a+b \end{array}\right| \begin{aligned} x+y-3 z+w &=& 2 \\ 2 x-y-3 z-2 w &=&-5 \\ x-3 y+z+4 w &=&-10 \\ 3 x+4 y-10 z-7 w &=& 9 \end{aligned} (ii) Prove, without expanding that (c) (i) Represent the following system of equations as an augmented matrix. (ii) Reduce the matrix in (c)(i) to row echelon form, find the rank and hence show that the system of equations admit an infinite number of solutions.Find a general solution for this system.

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