Advertisements
Advertisements
प्रश्न
Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
उत्तर
|A| = cos θ (cos θ) – sin θ (– sin θ)
= cos2θ + sin2θ
= 1 ≠ 0
∴ A–1 exists.
A11 = (–1)1+1 M11 = M11 = cos θ
A12 = (–1)1+2 M12 = – M12 = sin θ
A21 = (–1)2+1 M21 = – M21 = – sin θ
A22 = (–1)2+2 M22 = M22 = cos θ
∴ adj (A) = `[(cos theta, sin theta),(-sin theta, cos theta)]^"T"`
= `[(cos theta, -sin theta),(sintheta, cos theta)]`
∴ A–1 = `1/|"A"|` adj (A)
= `[(cos theta, -sin theta),(sin theta, cos theta)]`
संबंधित प्रश्न
Find the inverse of the following matrix by elementary row transformations if it exists.
`A = [(1, 2, -2), (0, -2, 1), (-1, 3, 0)]`
Find the co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
Find the matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I
Find the inverse of the following matrix.
`[(0,1,2),(1,2,3),(3,1,1)]`
Find the inverse of the following matrix.
`[(2,0,-1),(5,1,0),(0,1,3)]`
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,-3,3),(2,2,3),(3,-2,2)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(2,-4),(3,1)]`, then the adjoint of matrix A is
Choose the correct answer from the given alternatives in the following question:
If A = `[(1,2),(3,4)]`, and A (adj A) = kI, then the value of k is
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____
Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -1)]`.
Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.
Adjoint of `[(2, -3),(4, -6)]` is _______
Choose the correct alternative.
If a 3 x 3 matrix B has it inverse equal to B, thenB2 = _______
Fill in the blank :
If A = [aij]2x3 and B = [bij]mx1 and AB is defined, then m = _______
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:
`[(1, 1),(1, 1)]`
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]`, then A10 = ______
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If A = `[(0, 4, 3),(1, -3, -3),(-1, 4, 4)]`, then find A2 and hence find A−1
If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method
Complete the following activity to find inverse of matrix using elementary column transformations and hence verify.
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]` B−1 = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
C1 → C1 + C3
`[("( )", 0, -1),("( )", 1, 0),("( )", 1, 3)]` B−1 = `[("( )", 0, 0),("( )", 1, 0),("( )", 0, 1)]`
C3 → C3 + C1
`[(1, 0, 0),("( )", 1, "( )"),(3, 1, "( )")]` B−1 = `[(1, 0, "( )"),(0, 1, 0),("( )", 0, "( )")]`
C1 → C1 – 5C2, C3 → C3 – 5C2
`[(1, "( )", 0),(0, 1, 0),("( )", 1, "( )")]` B−1 = `[(1, 0, "( )"),("( )", 1, -5),(1, "( )", 2)]`
C1 → C1 – 2C3, C2 → C2 – C3
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]` B−1 = `[(3, -1, "( )"),("( )", 6, -5),(5, "( )", "( )")]`
B−1 = `[("( )", "( )", "( )"),("( )", "( )", "( )"),("( )", "( )", "( )")]`
`[(2, "( )", -1),("( )", 1, 0),(0, 1, "( )")] [(3, "( )", "( )"),("( )", 6, "( )"),("( )", -2, "( )")] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
adj (AB) is equal to:
The inverse matrix of `((3,1),(5,2))` is
The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?
The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A-1 is ______.
If A = `[(2, 2),(4, 5)]` and A–1 = λ(adj(A)), then λ = ______ .
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 = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
Find the inverse of the matrix A by using adjoint method.
where A = `[(-3, -1, 1),(0, 0, 1),(-15, 6, -6)]`
A–1 exists if |A| = 0.
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 = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.
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 = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0
