Advertisements
Advertisements
प्रश्न
Find the cofactor matrix, of the following matrices : `[(1, 2),(5, -8)]`
उत्तर
The co-factor Aij of aij is equal to (– 1)i+j Mij.
Here,
a11 = 1
∴ M11 = – 8
and A11 = (– 1)1+2 M11 = (1) (– 8) = – 8
a12 = 2
∴ M11 = 5
and A12 = (– 1)1+2 M12 = (– 1) (5) = – 5
a21 = 5
∴ M21 = 2
and A21 = (– 1)2+1 M21 = (– 1) (2) = – 2
a22 = – 8
∴ M22 = 1
and A22 = (– 1)2+2 M22 = (1) (1) = 1
∴ The matrix of the co-factors is
[Aij]2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)]`
= `[(-8, -5),(-2, 1)]`.
APPEARS IN
संबंधित प्रश्न
Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.
Using the properties of determinants, solve the following for x:
`|[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=0`
Using properties of determinants, prove that :
`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`
x + y + z + w = 2
x − 2y + 2z + 2w = − 6
2x + y − 2z + 2w = − 5
3x − y + 3z − 3w = − 3
Using elementary row operations, find the inverse of the matrix A = `((3, 3,4),(2,-3,4),(0,-1,1))` and hence solve the following system of equations : 3x - 3y + 4z = 21, 2x -3y + 4z = 20, -y + z = 5.
Apply the given elementary transformation on each of the following matrices `[(3, -4),(2, 2)]`, R1 ↔ R2.
Apply the given elementary transformation on each of the following matrices `[(2, 4),(1, -5)]`, C1 ↔ C2.
Find the adjoint of the following matrices : `[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Choose the correct alternative.
If A = `[("a", 0, 0),(0, "a", 0),(0, 0,"a")]`, then |adj.A| = _______
The suitable elementary row transformation which will reduce the matrix `[(1, 0),(2, 1)]` into identity matrix is ______
Find the inverse of matrix A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by using elementary row transformations
The cofactors of the elements of the first column of the matrix A = `[(2,0,-1),(3,1,2),(-1,1,2)]` are ______.
If `overlinea = hati + hatj + hatk, overlinea . overlineb = 1` and `overlinea xx overlineb = hatj - hatk,` then `overlineb` = ______
The inverse of a symmetric matrix is ______.
If possible, find BA and AB, where A = `[(2, 1, 2),(1, 2, 4)]`, B = `[(4, 1),(2, 3),(1, 2)]`
If A = `[(0, -1, 2),(4, 3, -4)]` and B = `[(4, 0),(1, 3),(2, 6)]`, then verify that: (kA)' = (kA')
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, -1, 3),(-5, 3, 1),(-3, 2, 3)]`
A matrix denotes a number.
if `A = [(2,5),(1,3)] "then" A^-1` = ______
If `[(3,0),(0,2)][(x),(y)] = [(3),(2)], "then" x = 1 "and" y = -1`
