Advertisements
Advertisements
Question
If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.
Solution
A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|`
`= 3|(6,-5),(-2,2)| + 1|(-15,-5),(5,2)| + 1|(-15,6),(5,-2)|`
= 3(12 - 10) + 1(- 30 + 25) + 1(30 - 30)
= 6 - 5 = 1 ≠ 0
∴ A-1 exists.
adj A = `[(+|(6,-5),(-2,2)|, -|(-15,-5),(5,2)|, +|(-15,6),(5,-2)|),(-|(-1,1),(-2,2)|, +|(3,1),(5,2)|, -|(3,-1),(5,-2)|),
(+|(-1,1),(6,-5)|, -|(3,1),(-15,-5)|, +|(3,-1),(-15,6)|)]^"T"`
`= [(+(12-10),-(-30 + 25),+(30-30)),(-(-2+2),+(6-5),-(-6+5)),(+(5-6),-(-15+15),+(18-15))]^"T"`
`= [(2,5,0),(0,1,1),(-1,0,3)]^"T"`
`= [(2,0,-1),(5,1,0),(0,1,3)]`
Now, `"A"^-1 = 1/|"A"|`adj A
`= 1/1 [(2,0,-1),(5,1,0),(0,1,3)] = [(2,0,-1),(5,1,0),(0,1,3)]`
APPEARS IN
RELATED QUESTIONS
Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`
Find the inverse of the following matrix.
`[(2,0,-1),(5,1,0),(0,1,3)]`
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
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
If A = `[(1, -1, 1),(2, 1, -3),(1, 1, 1)]`, 10B = `[(4, 2,2),(-5, 0, ∞),(1, -2, 3)]` and B is the inverse of matrix A, then α = ______
Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`
The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.
If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______
If A = `[(-i, 0),(0, i)]`, then ATA is equal to
If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I
