Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let A = `[(1,−1,2),(2,1,3),(3,2,4)]`
C1 → C1 − C2
A ∼ `[(0,−1,2),(3,1,3),(5,2,4)]`
C1 ↔ C2
`[(-1,0,2),(1,3,3),(2,5,4)]`
C2 → C2 + 3C1, C3 → C3 + 2C1
`[(-1,0,0),(1,6,5),(2,11,8)]`
C3 → 6C3 − 5C2
`[(-1,0,0),(1,6,0),(2,11,-7)]`
C1 ↔ C3
`[(0,0,-1),(0,6,1),(-7,11,2)]`
APPEARS IN
संबंधित प्रश्न
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 = `[(5,4),(1,3)]`, C1↔ C2; B = `[(3,1),(4,5)]` R1↔ R2.
What do you observe?
Apply the given elementary transformation of the following matrix.
A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2
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.
Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row 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:
`[(1,0),(0,1)]`
Check whether the following matrix is invertible or not:
`((1,1),(1,1))`
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:
`(("sec" theta , "tan" theta),("tan" theta,"sec" theta))`
If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`
If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.
Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row transformations.
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, find AB and (AB)-1 . Verify that (AB)-1 = B-1.A-1.
Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`
Find the inverse of A = `[(1,0,1),(0,2,3),(1,2,1)]` by using elementary column transformations.
Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.
Choose the correct answer from the given alternatives in the following question:
If A = `[(1,2),(3,4)]` , adj A = `[(4,"a"),(-3,"b")]`, then the values of a and b are
Choose the correct answer from the given alternatives in the following question:
The inverse of `[(0,1),(1,0)]` is
Choose the correct answer from the given alternatives in the following question:
If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is
If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2
Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`
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 matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)−1
If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A–1
