Advertisements
Advertisements
Question
Check whether the following matrix is invertible or not:
`((1,2),(3,3))`
Solution
Let A = `((1,2),(3,3))`
Then, |A| = `|(1,2),(3,3)| = 3 - 6 = - 3 ≠ 0`
∴ A is a non - singular matrix.
Hence, A-1 exists.
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.
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.
Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.
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 = `[(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:
`((2,3),(10,15))`
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)]`
Find the matrix X such that AX = B, where A = `[(1,2),(-1,3)]` and B = `[(0,1),(2,4)]`
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.
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:
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:
If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k 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, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2
If A = `[(-2, 4),(-1, 2)]` then 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)]`
Find A−1 using column transformations:
A = `[(2, -3),(-1, 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)]`
Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.
Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.
