Question

# for 10-12 you will solve the following system of equations: 2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is...

for 10-12 you will solve the following system of equations: 2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is the solution for x? a)2 b)-3 c)infinitely many solutions d)no solution 11) what is the solution for y? a)2 b)0 c)inifinitely many solution d)no solution 12) what is the solution for z? a)4 b)-8 c)infinitely many solutions d)no solutions

The given system of equations is 2x+y+z=-2…(1), 2x-y+3z=6 …(2) and3x-5y+4z=7…(3).

The augmented matrix of this linear system is A (say) =

 2 1 1 -2 2 -1 3 6 3 -5 4 7

To solve the given system of equations, we will reduce A to its RREF as under:

Multiply the 1st row by ½

Add -2 times the 1st row to the 2nd row

Add -3 times the 1st row to the 3rd row

Multiply the 2nd row by -1/2

Add 13/2 times the 2nd row to the 3rd row

Multiply the 3rd row by -1/4

Add 1 times the 3rd row to the 2nd row

Add -1/2 times the 3rd row to the 1st row

Add -1/2 times the 2nd row to the 1st row

Then the RREF of A is

 1 0 0 -3 0 1 0 0 0 0 1 4

This implies that the given system of equations has a unique solution x = -3, y = 0 and z = 4.

10) b

11) b

12) a

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