Advertisements
Advertisements
प्रश्न
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
उत्तर
Let A = `[[2,-2],[4,3]]`
|A|= `|[2,-2],[4,3]|` = 6 + 8 = 14 `≠` 0
∴ A−1 exist
First we have to find the co-factor matrix
= [Aij]2×2′, where Aij = (−1)i+jMij
Now, A11 = (− 1)1+1M11 = 3
A12 = (− 1)1+2M12 = − 4
A21 = (− 1)2+1M21 = (− 2) = 2
A22 = (− 1)2+2M22 = 2
Hence, the co-factor matrix
= `[("A"_11,"A"_12),("A"_21,"A"_22)]` = `[(3,-4),(2,2)]`
∴ adj A `=[(3,2),(-4,2)]`
∴ A−1 = `1/|"A"|` (adj A) = `1/14[(3,2),(-4,2)]`
APPEARS IN
संबंधित प्रश्न
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.
`[(-1,5),(-3,2)]`
Find the inverse of the following matrix.
`[(2, -3),(-1, 2)]`
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:
If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____
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 = _______
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
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 = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` is ______
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 = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
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
If A is an invertible matrix of order 2 then det (A-1) be equal
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.
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?
If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A−1 = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.
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 A–1 = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = ______.
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
If A = `[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`, then A2008 is equal to ______.
The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
If A = `[(cos α, sin α),(- sin α, cos α)]`, then the matrix A is ______.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0
