Advertisements
Advertisements
प्रश्न
Find the co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
उत्तर
Let A = `[(-1, 2),(-3, 4)]`
Here, a11 = −1, M11 = 4
∴ A11 = (−1)1+1(4) = 4
a12 = 2, M12 = −3
∴ A12 = (−1)1+2(−3) = 3
a21 = −3, M21 = 2
∴ A21 = (−1)2+1(2) = −2
a22 = 4, M22 = −1
∴ A22 = (−1)2+2(−1) = −1
संबंधित प्रश्न
Find the adjoint of the following matrix.
`[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix (if they exist):
`[(2,-3),(5,7)]`
Find the inverse of the following matrix (if they exist):
`[(2,-3,3),(2,2,3),(3,-2,2)]`
Choose the correct answer from the given alternatives in the following question:
For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals
Adjoint of `[(2, -3),(4, -6)]` is _______
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
Fill in the blank :
If A = [aij]2x3 and B = [bij]mx1 and AB is defined, then m = _______
State whether the following is True or False :
Singleton matrix is only row matrix.
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
Check whether the following matrices are invertible or not:
`[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______
A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
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)]`
If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method
Complete the following activity to verify A. adj (A) = det (A) I.
Given A = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)]` then
|A| = 2(____) – 0(____) + ( ) (____)
= 6 – 0 – 5
= ______ ≠ 0
Cofactors of all elements of matrix A are
A11 = `(-1)^2 |("( )", "( )"),("( )", "( )")|` = (______),
A12 = `(-1)^3 |(5, "( )"),("( )", 3)|` = – 15,
A13 = `(-1)^4 |(5, "( )"),("( )", 1)|` = 5,
A21 = _______, A22 = _______, A23 = _______,
A31 = `(-1)^4 |("( )", "( )"),("( )", "( )")|` = (______),
A32 = `(-1)^5 |(2, "( )"),("( )", 0)|` = ( ),
A33 = `(-1)^6 |(2, "( )"),("( )", 1)|` = 2,.
Cofactors of matrix A = `[(3, "____", "____"),("____", "____",-2),(1, "____", "____")]`
adj (A) = `[("____", "____", "____"),("____", "____","____"),("____","____","____")]`
A.adj (A) = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)] [("( )", -1, 1), (-15, "( )", -5),("( )", -2, "( )")] = [(1, 0, "( )"),("( )", "( )", "( )"),(0, "( )", "( )")]` = |A|I
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
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:
x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4
Solve by matrix inversion method:
2x – z = 0; 5x + y = 4; y + 3z = 5
If A and B non-singular matrix then, which of the following is incorrect?
The cost of 2 Kg of Wheat and 1 Kg of Sugar is ₹ 70. The cost of 1 Kg of Wheat and 1 Kg of Rice is ₹ 70. The cost of 3 Kg of Wheat, 2 Kg of Sugar and 1 Kg of rice is ₹ 170. Find the cost of per kg each item using the matrix inversion method.
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______
If AB = I and B = AT, then _______.
If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A11, A11, A13 are co-factors of a11, a12, a13 respectively, then the value of a11A11 + a12A12 + a13A13 = ______.
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
Find the inverse of the matrix A by using adjoint method.
where A = `[(-3, -1, 1),(0, 0, 1),(-15, 6, -6)]`
If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is ______.
The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.
If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.
If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B–1 A–1)–1 is equal to ______.
If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.
For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.
If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I
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`
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0
