Answer:
D.(1,5,2)
Step-by-step explanation:
Lets write the augmented matrix by writing the coefficients of all the variables
3 -4 -5 -27 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
WE need to get
1 0 0
0 1 0
0 0 1 then last column will be the value of x , y , z
To get identity matrix we use row operations
(R1=R1/3)
1 -4/3 -5/3 -9 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
Subtract row 1 multiplied by 5 from row 2 (R2=R2−(5)R1)
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
5 -4 4 -7 Row 3
Subtract row 1 multiplied by 5 from row 3 (R3=R3−(5)R1)
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
0 8/3 37/3 38 Row 3
Multiply row 2 by 326 (R2=(3/26)R2)
1 -4/3 -5/3 -9 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Subtract row 2 multiplied by 8/3 from row 3 (R3=R3−(8/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 135/13 270/13 Row 3
Multiply row 3 by 13/135 (R3=(13/135)R3)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)
1 0 0 1 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Subtract row 3 multiplied by 19/26 from row 2 (R2=R2−(19/26)R3)
1 0 0 1 Row 1
0 1 0 5 Row 2
0 0 1 2 Row 3
From the above matrix we can say that x=1 , y=5 and z= 2
