Advertisements
Advertisements
Question
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
Solution
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = – 1.
APPEARS IN
RELATED QUESTIONS
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)]`
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
Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -1)]`.
If A is a no singular matrix, then det (A–1) = _______
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.
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
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 = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
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:
`[(1,2,3),(0,2,4),(0,0,5)]`
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
Show that the matrices A = `[(2,2,1),(1,3,1),(1,2,2)]` and B = `[(4/5,(-2)/5,(-1)/5),((-1)/5,3/5,(-1)/5),((-1)/5,(-2)/5,4/5)]` are inverses of each other.
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.
adj (AB) is equal to:
Which of the following matrix has no inverse
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.
If A = `[(1,2),(3,-5)]`, then A-1 = ?
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______
If A and Bare square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| = ______.
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` 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 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 = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0