(a) Write the following system of equations in a matrix form of $Avec{x} = vec{b}$: $x - y + z = 4$ $2x + y - z = -1$ $3x + 2y + 2z = 5$ (b) Use Cramer's rule to solve for $y$. (c) calculate the cofactor matrix of $A$ by hand. (d) Using the cofactor matrix, calculate the matrix inverse and use that to solve the above system of equations.
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