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

If A = [123-2-10] and B = [1324-13] then find the order of AB - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

बेरीज

उत्तर

A = `[(1, 2),(3, -2),(1, 0)]` is 3 × 2 matrix and B = `[(1, 3, 2),(4, -1, 3)]` is 2 × 3 matrix

∴ AB is 3 × 3 matrix

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.2: Matrics - Very Short Answer

संबंधित प्रश्‍न

 Find the inverse of the following matrix by elementary row transformations if it exists. `A=[[1,2,-2],[0,-2,1],[-1,3,0]]`


The sum of three numbers is 6. If we multiply the third number by 3 and add it to the second number we get 11. By adding first and third numbers we get a number, which is double than the second number. Use this information and find a system of linear equations. Find these three numbers using matrices.


If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.


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


Find the adjoint of the following matrix.

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


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

`[(2,-3),(5,7)]`


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


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


Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.


Choose the correct alternative.

If AX = B, where A = `[(-1, 2),(2, -1)], "B" = [(1),(1)]`, then X = _______


Adjoint of `[(2, -3),(4, -6)]` 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),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'


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


Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`


If A = `[(0, 4, 3),(1, -3, -3),(-1, 4, 4)]`, then find A2 and hence find A−1 


Choose the correct alternative:

If A is a non singular matrix of order 3, then |adj (A)| =  ______


The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` is ______


Find the inverse of the following matrix:

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


Solve by matrix inversion method:

2x – z = 0; 5x + y = 4; y + 3z = 5


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


The cost of 2 Kg of Wheat and 1 Kg of Sugar is ₹ 70. The cost of 1 Kg of Wheat and 1 Kg of Rice is ₹ 70. The cost of 3 Kg of Wheat, 2 Kg of Sugar and 1 Kg of rice is ₹ 170. Find the cost of per kg each item using the matrix inversion method.


If A = `[(1,2),(3,-5)]`, then A-1 = ?


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


If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______ 


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


The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.


If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.


The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.


If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.


If A = `[(cos α, sin α),(-sin α, cos α)]`, then find α satisfying `0 < α < π/2`, when A + AT = `sqrt(2)  l_2` where AT is transpose of A.


If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`

Find (AB)–1 by adjoint method.

Solution:

AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`

AB = [  ]

|AB| =  `square`

M11 = –2  ∴ A11 = (–1)1+1 . (–2) = –2

M12 = –3     A12 = (–1)1+2 . (–3) = 3

M21 = 4       A21 = (–1)2+1 . (4) = –4

M22 = 3       A22 = (–1)2+2 . (3) = 3

Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`

adj (A) = [  ]

A–1 = `1/|A| . adj(A)`

A–1 = `square`


If A = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×