Advertisements
Advertisements
Question
If A-1 = `[(1,0,3),(2,1,-1),(1,-1,1)]` then, find A.
Solution
Given A-1 = `[(1,0,3),(2,1,-1),(1,-1,1)]`
We know that (A-1)-1 = A
So we have to find inverse of A-1
`|"A"^-1| = |(1,0,3),(2,1,-1),(1,-1,1)|`
= 1(1 - 1)- 0(2 + 1) + 3(-2 - 1)
= 1(0) - 0(03 + 3(-3)
= 0 - 0 - 9 = - 9 ≠ 0
`["A"_"ij"^-1] = [(0,-3,-3),
(-|(0,3),(-1,1)|,|(1,3),(1,1)|,-|(1,0),(1,-1)|),
(|(0,3),(1,-1)|,-|(1,3),(2,-1)|,|(1,0),(2,1)|)]`
= `[(0,-3,-3),(-(0+3),1-3,-(-1-0)),(0-3,-(-1-6),(1-0))]`
`= [(0,-3,-3),(-3,-2,1),(-3,7,1)]`
adj A-1 = `["A"_"ij"^-1]^"T" = [(0,-3,-3),(-3,-2,7),(-3,1,1)]`
∴ (A-1)-1 = `1/|"A"^-1|` (adj A-1)
`= 1/(-9)[(0,-3,-3),(-3,-2,7),(-3,1,1)]`
i.e., A = `1/9[(0,3,3),(3,2,-7),(3,-1,-1)]`
APPEARS IN
RELATED QUESTIONS
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 = _____
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 :
If A and B are conformable for the product AB, then (AB)T = ATBT.
If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = ______
If `A = [[-3,1],[-4,3]]` and A-1 = αA, then α = ______.
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
