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(Solved): Consider the following system of linear equations x-3y+2z+3w=1 2x-4y+3z+a^(2)w=-1 -3x+y+az-w=b whe ...



Consider the following system of linear equations

x-3y+2z+3w=1 2x-4y+3z+a^(2)w=-1 -3x+y+az-w=b

where

a

and

b

are real numbers. Using Gaussian elimination, determine all possible values of

a

and

b

such that the system has (a) no solution; (b) infinitely many solutions with one free variable; (c) infinitely many solutions with two free variables. Then solve the system in part (c).



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