Practice set eight

 Using Cramer's rule find \(x,y\;\) and \(\;z\) for the following system of equations


1).  \( x+y+z=1,\)\(\;2x+2y+2z=2,\)\(\;3x+3y+3z=4.\)

2).  \(3x+4y+5z=40,\;\)\(\; 2x-3y+4y=13,\) \(\; x+y+z=9\)

3).  \(3x-2y+3z=8,\;\) \(\;2x+y-z=1,\)\(\;4x-3y+2z=4\)

4).  \(-y+4z=23,\;\) \(\;2x+5y=13,\)\(\;-5x+3z=51\)

5).  \(2x-5z+3y=1,\;\) \(\;x+y-z-2=0,\)\(\;z+2y=8\)






Answers:

1). Inconsistent (because the rank of [A:b] is not same as that of A)

2). \(x=1,y=3,z=5\)

3). \(x=1,y=2,z=3\)

4). \(x=-6,y=5,z=7\)

5). \(x=1,y=3,z=2\)

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