Advertisements
Advertisements
प्रश्न
If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.
उत्तर
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
संबंधित प्रश्न
Find matrix X, if AX = B, where A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "and B" = [(1),(2),(3)]`.
Check whether the following matrices are invertible or not:
`[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
Choose the correct alternative:
If A is a non singular matrix of order 3, then |adj (A)| = ______
Find the inverse of matrix B = `[(3,1, 5),(2, 7, 8),(1, 2, 5)]` by using adjoint method
If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
If A = `[(cos α, sin α),(- sin α, cos α)]`, then the matrix A is ______.
