Advertisements
Advertisements
Question
Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
Solution
Given that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
Applying R2 → R2 – 2R1 and R3 → R3 – R1, we get
`[(1, 2, 3),(0, -1, -4),(0, 0,-1)]` X = `[(2, 2, -5),(-6, -5, 14),(-1, -2, 4)]`
Applying R2 → R2 – 4R3, we get
`[(1, 2, 3),(0, -1, 0),(0, 0,-1)]` X = `[(2, 2, -5),(-2, 3, -2),(-1, -2, 4)]`
Applying R1 → R1 + 2R2, we get
`[(1, 0, 3),(0, -1, 0),(0, 0,-1)]` X = `[(-2, 8, -9),(-2, 3, -2),(-1, -2, 4)]`
Applying R1 → R1 + 3R3, we get
`[(1, 0, 0),(0, -1, 0),(0, 0,-1)]` X = `[(-5, 2, 3),(-2, 3, -2),(-1, -2, 4)]`
Applying R2 → (–1)R2 and R3 → (–1)R3, we get
`[(1, 0, 0),(0, 1, 0),(0, 0,1)]` X = `[(-5, 2, 3),(2, -3, 2),(1, 2, -4)]`
∴ X = `[(-5, 2, 3),(2, -3, 2),(1, 2, -4)]`
APPEARS IN
RELATED QUESTIONS
Apply the given elementary transformation of the following matrix.
A = `[(1,0),(-1,3)]`, R1↔ R2
Apply the given elementary transformation of the following matrix.
B = `[(1, -1, 3),(2, 5, 4)]`, R1→ R1 – R2
Apply the given elementary transformation of the following matrix.
A = `[(1,2,-1),(0,1,3)]`, 2C2
B = `[(1,0,2),(2,4,5)]`, −3R1
Find the addition of the two new matrices.
Apply the given elementary transformation of the following matrix.
A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2
and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C3 + 2C2 and then 3R3
What do you conclude?
Apply the given elementary transformation of the following matrix.
Use suitable transformation on `[(1,2),(3,4)]` to convert it into an upper triangular matrix.
Apply the given elementary transformation of the following matrix.
Transform `[(1,-1,2),(2,1,3),(3,2,4)]` into an upper triangular matrix by suitable column transformations.
If A = `((1,0,0),(2,1,0),(3,3,1))`, then reduce it to I3 by using column transformations.
If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I3 by using row transformations.
Check whether the following matrix is invertible or not:
`((1,1),(1,1))`
Check whether the following matrix is invertible or not:
`((1,2),(3,3))`
Check whether the following matrix is invertible or not:
`((2,3),(10,15))`
Check whether the following matrix is invertible or not:
`[(cos theta, sin theta),(-sin theta, cos theta)]`
Check whether the following matrix is invertible or not:
`((1,2,3),(2,-1,3),(1,2,3))`
Check whether the following matrix is invertible or not:
`((1,2,3),(3,4,5),(4,6,8))`
If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, find AB and (AB)-1 . Verify that (AB)-1 = B-1.A-1.
If A = `[(4,5),(2,1)]`, show that `"A"^-1 = 1/6("A" - 5"I")`.
Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`
If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C
Find A-1 by the adjoint method and by elementary transformations, if A = `[(1,2,3),(-1,1,2),(1,2,4)]`
Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.
Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3) "is" "a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|`
If A = `[(1,0,1),(0,2,3),(1,2,1)]` and B = `[(1,2,3),(1,1,5),(2,4,7)]`, then find a matrix X such that XA = B.
Find the inverse of the following matrix (if they exist).
`[(1,3,-2),(-3,0,-5),(2,5,0)]`
Choose the correct answer from the given alternatives in the following question:
The inverse of `[(0,1),(1,0)]` is
The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.
If A = `[(-2, 4),(-1, 2)]` then find A2
Find A−1 using column transformations:
A = `[(5, 3),(3, -2)]`
If A = `[(1, 2, -1),(3, -2, 5)]`, apply R1 ↔ R2 and then C1 → C1 + 2C3 on A
Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.
