Solve the following using the cramer method

Question

2x-y+z=3
2y-z=1
-x+y=1

a)x=2;y=1;z=3
b)x=1;y=2;z=3
c)x=3;y=-2;z=-3

Answer 1

The given equations are 2x-y+z=3 , 2y -z =1, -x +y =1.

The above equations can be written in matrix  form as

Let 

det A = 2[ 2(0) - (-1) (1) ] - (-1) [ 0(0)-(-1)(-1) ] + 1[ 0(1) - 2(-1) ]

 = 2 -1+2  = 3

Replace by first column  with Y

det X1 = 3 [ 2(0) - (-1)(1) ] -(-1) [ 1(0) -(-1)(1) ] +1[1(1) -2(1)]

= 3 +1-1 = 3

Replace by second column with Y

det X2 = 2[ 1(0) -(-1)(1) ] -3 [0(0) -(-1)(-1) ] +1[ 0(1) -1(-1) ]

= 2+3+1 = 6

det X3 = 2 [ 2(1) -1(1) ] - (-1) [0(1) -1(-1)] +3 [0(1) -2(-1) ]

= 2+1+6 = 9

Therefore the value of  x = det X1/ det A = 3/3 =1

y = det X2 / det A  = 6/3 = 2

z = det X3 / det A = 9/3 = 3

Option  b is  the  right  answer.