मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the cofactors of the elements of the matrix [-12-34] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the cofactors of the elements of the matrix

`[(-1, 2),(-3, 4)]`

बेरीज

उत्तर

Given, matrix is `[(-1, 2),(-3, 4)]`

Here a11 = –1; ∴ N11 = 4 and A11 = (–1)1+1 (4) = 4

a12 = 2; ∴ N12 = –3 and A12 = (–1)1+2 (–3) = 3

a21 = –3; ∴ N21 = 2 and A21 = (–1)2+1 (2) = –2

a22 = 4; ∴ N22 = –1 and A22 = (–1)2+2 (–1) = –1

∴ The required cofactors are 4, 3, –2, –1.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2021-2022 (March) Set 1

संबंधित प्रश्‍न

Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.


Find the matrix of the co-factor for the following matrix.

`[(1,3),(4,-1)]`


If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I


Find the inverses of the following matrices by the adjoint method:

`[(1,2,3),(0,2,4),(0,0,5)]`


Find the inverse of the following matrix (if they exist):

`((1,-1),(2,3))`


Find the inverse of the following matrix (if they exist):

`[(2,0,-1),(5,1,0),(0,1,3)]`


Choose the correct answer from the given alternatives in the following question:

If A = `[(2,-4),(3,1)]`, then the adjoint of matrix A 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 = _____


Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.


Find the inverse of  A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by elementary column transformations.


Choose the correct alternative.

If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______


If A is a no singular matrix, then det (A–1) = _______


Fill in the blank :

If A = `[(3, -5),(2, 5)]`, then co-factor of a12 is _______


Fill in the blank :

If A = [aij]mxm is a non-singular matrix, then A–1 = `(1)/(......)` adj(A).


Fill in the blank :

If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______


Fill in the blank :

If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`


State whether the following is True or False :

If A and B are conformable for the product AB, then (AB)T = ATBT.


State whether the following is True or False :

A(adj. A) = |A| I, where I is the unit matrix.


Solve the following :

If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.


Find inverse of the following matrices (if they exist) by elementary transformations :

`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`


Find inverse of the following matrices (if they exist) by elementary transformations :

`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`


Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.


The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.


If ω is a complex cube root of unity, then the matrix A = `[(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)]` is


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 = ______


If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB


A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)


If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)


Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`


Find the adjoint of the matrix A = `[(2,3),(1,4)]`


Find the inverse of the following matrix:

`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`


If A-1 = `[(1,0,3),(2,1,-1),(1,-1,1)]`  then, find A.


Solve by matrix inversion method:

3x – y + 2z = 13; 2x + y – z = 3; x + 3y – 5z = - 8


Solve by matrix inversion method:

x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4


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.


Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.

Week Number of employees Total weekly salary
(in ₹)
A B C
1st week 4 2 3 4900
2nd week 3 3 2 4500
3rd week 4 3 4 5800

adj (AB) is equal to:


The inverse matrix of `((3,1),(5,2))` is


If A = `((-1,2),(1,-4))` then A(adj A) is


If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B-1A-1 = ?


If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______ 


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 and Bare square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| = ______.


If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______ 


If A2 - A + I = 0, then A-1 = ______.


If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.


If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.


If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.


For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×