Advertisements
Advertisements
प्रश्न
Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.
उत्तर
Let A = `[(2, -2),(4, 5)]`
∴ |A| = `[(2, -2),(4, 5)]` = 10 + 8 = 18 ≠ 0
∴ A–1 exists.
A11 = (– 1)1+1 M11 = (1)(5) = 5
A12 = (– 1)1+2 M12 = (– 1)(4) = – 4
A21 = (– 1)2+1 M21 = (– 1)(– 2) = 2
A22 = (– 1)2+2 M22 = (1)(2) = 2
∴ The matrix of the co-factors is
[Aij]2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)] = [(5, -4),(2, 2)]`
Now adj A = `["A"_"ij"]_(2xx2)^"T" = [(5, 2),(-4, 2)]`
∴ A–1 = `(1)/|"A"|("adj A")`
= `(1)/(18)[(5, 2),(-4, 2)]`.
APPEARS IN
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,-1,2),(-2,3,5),(-2,0,-1)]`
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
Find the adjoint of the following matrix.
`[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverse of the following matrix by the adjoint method.
`[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`
Find the inverse of the following matrix (if they exist):
`((2,1),(1,-1))`
Find the inverse of A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by elementary column transformations.
Choose the correct alternative.
If AX = B, where A = `[(-1, 2),(2, -1)], "B" = [(1),(1)]`, then X = _______
If A is a no singular matrix, then det (A–1) = _______
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
Check whether the following matrices are invertible or not:
`[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
A = `[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0, 0, 1)]`, then A−1 is
If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
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)]`
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
Find the inverse of the following matrix:
`[(3,1),(-1,3)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.
| Months | Sales in units | Commission | ||
| A | B | C | ||
| January | 9 | 10 | 2 | 800 |
| February | 15 | 5 | 4 | 900 |
| March | 6 | 10 | 3 | 850 |
Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
If A is an invertible matrix of order 2 then det (A-1) be equal
If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-1.
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 [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
If ω is a complex cube root of unity and A = `[(ω,0,0),(0,ω^2,0),(0,0,1)]` then A-1 = ?
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
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)]`
If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B–1 A–1)–1 is equal to ______.
