Advertisements
Advertisements
प्रश्न
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
उत्तर
– 2
APPEARS IN
संबंधित प्रश्न
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Find the matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
State whether the following is True or False :
A(adj. A) = |A| I, where I is the unit matrix.
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
If ω is a complex cube root of unity, then the matrix A = `[(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)]` is
If A = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]`, then A10 = ______
If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______
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
Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
If A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`, then verify that (AB)-1 = B-1A-1
The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
If A = `[(a,b),(c,d)]` such that ad - bc ≠ 0 then A-1 is
If A = `((-1,2),(1,-4))` then A(adj A) is
The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.
If A is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A-1 = ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If A = `[(2, 2),(4, 5)]` and A–1 = λ(adj(A)), then λ = ______ .
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
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 ______.
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 inverse of the matrix A by using adjoint method.
where A = `[(-3, -1, 1),(0, 0, 1),(-15, 6, -6)]`
If A = `[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`, then A2008 is equal to ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
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 A and B are two square matrices such that A2B = BA and (AB)10 = AkB10. Then, k is ______.
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`
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
