Advertisement Remove all ads

Express the following equations in the matrix form and solve them by method of reduction : 2x- y + z = 1, x + 2y + 3z = 8, 3x + y - 4z =1 - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

Express the following equations in the matrix form and solve them by method of reduction :

2x- y + z = 1, x + 2y + 3z = 8, 3x + y - 4z =1

Advertisement Remove all ads

Solution

The matrix form of given equations is

`[[2,-1,1],[1,2,3],[3,1,-4]][[x],[y],[z]]=[[1],[8],[1]]`

`R_1 harr R_2`

`[[1,2,3],[2,-1,1],[3,1,-4]][[x],[y],[z]]=[[8],[1],[1]]`

`R_2-> R_2+R_1`

`[[1,2,3],[3,1,4],[3,1,-4]][[x],[y],[z]]=[[8],[9],[1]]`

`R_3 -> R_3-R_2`

`[[1,2,3],[3,1,4],[0,0,-8]][[x],[y],[z]]=[[8],[9],[-8]]`

`R_2->R_2-3R_1`

`[[1,2,3],[0,-5,-5],[0,0,-8]][[x],[y],[z]]=[[8],[-15],[-8]]`

`[[x+2y+3z],[-5y-5z],[-8z]]=[[8],[-15],[-8]]`

therefore

x + 2y + 3z = 8 .............(1)

-5y -5z = -15....... (2)

-8z = -8..............(3)

From (3),

z = 1

From (2),

-5y - 5(1) = -15 ... (because z = 1)

-5y =-10

y = 2

From (1),

x + 2(2)+ 3(1) = 8 ... (because z = 1 and y = 2)

x = 8 -7

x = 1

Thus, x = 1, y = 2, z = 1

Concept: Elementary Transformations
  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×