Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

Find matrix X, if AX = B, where A = [123-112124]and B=[123]. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Find matrix X, if AX = B, where A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "and B" = [(1),(2),(3)]`.

Advertisement Remove all ads

Solution

Given,AX = B

∴ `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "X" = [(1),(2),(3)]`

Applying R2 → R2 + R1 and R3 → R3 – R1, we get

`[(1, 2, 3),(0, 3, 5),(0, 0, 1)] "X" = [(1),(2),(3)]`

Applying R2 → `(1/3)` R2, we get

`[(1, 2, 3),(0, 1, 5/3),(0, 0, 1)] "X" = [(1),(1),(2)]`

Applying R1 → R1 – 2R2 , we get

`[(1, 0, -1/3),(0, 1, 5/3),(0, 0, 1)] "X" = [(-1),(1),(2)]`

Applying R1 → R1 + `(1/3)` R3 and  R2 → R2 `-(5/3)` R3,  we get

`[(1, 0, 0),(0, 1, 0),(0, 0, 1)] "X" = [(-1/3),(-7/3),(2)]`

∴ X = `[(-1/3),(-7/3),(2)]`.

Concept: Inverse of Matrix
  Is there an error in this question or solution?
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×