Advertisements
Advertisements
Question
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
Solution
Let A = `((1,-1),(2,3))`
∴ |A| = `|(1,-1),(2,3)| = 3 + 2 = 5 ≠ 0`
∴ A-1 exists.
Consider AA-1 = I
∴ `((1,-1),(2,3)) "A"^-1 = ((1,0),(0,1))`
By R2 - 2R1, we get,
`((1,-1),(0,5)) "A"^-1 = ((1,0),(-2,1))`
By `(1/5) "R"_2`, we get,
`((1,-1),(0,1)) "A"^-1 = ((1,0),(-2/5,1/5))`
By R1 + R2, we get,
`((1,0),(0,1)) "A"^-1 = ((3/5,1/5),(-2/5,1/5))`
∴ A-1 = `1/5((3,1),(-2,1))`
APPEARS IN
RELATED QUESTIONS
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.
Find the co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
Find the co-factor of the element of the following matrix.
`[(1,-1,2),(-2,3,5),(-2,0,-1)]`
Find the inverse of the following matrix by the adjoint method.
`[(-1,5),(-3,2)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.
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.
Adjoint of `[(2, -3),(4, -6)]` is _______
Fill in the blank :
If A = [aij]mxm is a non-singular matrix, then A–1 = `(1)/(......)` adj(A).
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
If A(α) = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]` then prove that A2(α) = A(2α)
If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'
Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
If X = `[(8,-1,-3),(-5,1,2),(10,-1,-4)]` and Y = `[(2,1,-1),(0,2,1),(5,p,q)]` then, find p, q if Y = X-1
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
adj (AB) is equal to:
If A and B non-singular matrix then, which of the following is incorrect?
If A is an invertible matrix of order 2 then det (A-1) be equal
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.
If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A−1 = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.
The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.
Choose the correct option:
If X, Y, Z are non zero real numbers, then the inverse of matrix A = `[(x, 0, 0),(0, y, 0),(0, 0, z)]`
Find the cofactors of the elements of the matrix
`[(-1, 2),(-3, 4)]`
A–1 exists if |A| = 0.
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = ______.
If A = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.
If matrix A = `[(1, -1),(2, 3)]`, then A2 – 4A + 5I is where I is a unit matix.
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
