Advertisements
Advertisements
Question
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
Solution
(B−1 A−1)−1 = [(AB)−1]−1 .......[∵ (AB−1) = B−1 A−1]
= AB
∴ (B−1 A−1)−1 = `[(2, 2),(-3, 2)] [(0, -1),(1, 0)]`
= `[(0 + 2, -2 + 0),(0 + 2, 3 + 0)]`
= `[(2, -2),(2, 3)]`
APPEARS IN
RELATED QUESTIONS
The sum of three numbers is 6. If we multiply the third number by 3 and add it to the second number we get 11. By adding first and third numbers we get a number, which is double than the second number. Use this information and find a system of linear equations. Find these three numbers using matrices.
Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.
Find the inverse of the following matrix (if they exist):
`((2,1),(1,-1))`
Find the inverse of the following matrix (if they exist):
`((1,3),(2,7))`
Find the inverse of the following matrix (if they exist):
`[(2,-3),(5,7)]`
Choose the correct answer from the given alternatives in the following question:
The inverse of A = `[(0,1,0),(1,0,0),(0,0,1)]` is
Choose the correct answer from the given alternatives in the following question:
The inverse of a symmetric matrix is
Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.
Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.
Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
Check whether the following matrices are invertible or not:
`[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
The solution (x, y, z) of the equation `[(1, 0, 1),(-1, 1, 0),(0, -1, 1)] [(x),(y),(z)] = [(1),(1),(2)]` is (x, y, z) =
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B-1A-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 = `[(x,1),(1,0)]` and A = A , then x = ______.
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If AB = I and B = AT, then _______.
The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.
If A = `[(2, -3, 3),(2, 2, 3),(3, "p", 2)]` and A–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.
Find the cofactors of the elements of the matrix
`[(-1, 2),(-3, 4)]`
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B–1 A–1)–1 is equal to ______.
If A = `[(cos α, sin α),(-sin α, cos α)]`, then find α satisfying `0 < α < π/2`, when A + AT = `sqrt(2) l_2` where AT is transpose of A.
If A = `[(cos α, sin α),(- sin α, cos α)]`, then the matrix A is ______.
For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.
If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`
Find (AB)–1 by adjoint method.
Solution:
AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`
AB = [ ]
|AB| = `square`
M11 = –2 ∴ A11 = (–1)1+1 . (–2) = –2
M12 = –3 A12 = (–1)1+2 . (–3) = 3
M21 = 4 A21 = (–1)2+1 . (4) = –4
M22 = 3 A22 = (–1)2+2 . (3) = 3
Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`
adj (A) = [ ]
A–1 = `1/|A| . adj(A)`
A–1 = `square`
Find the inverse of the matrix `[(1, 1, 1),(1, 2, 3),(3, 2, 2)]` by elementary column transformation.
