English

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

Advertisements
Advertisements

Question

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

Sum

Solution

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
  Is there an error in this question or solution?
Chapter 1.2: Matrics - Very Short Answer

RELATED QUESTIONS

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


Find the adjoint of the following matrix.

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


Find the adjoint of the following matrix.

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


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


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


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

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


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


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

If A = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______


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 = _____


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

If A = `[("cos"alpha, - "sin"alpha,0),("sin"alpha,"cos"alpha,0),(0,0,1)]` where α ∈ R, then [F(α)]-1 is


If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.


Choose the correct alternative.

If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______


Fill in the blank :

(AT)T = _______


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

`[(2, 1),(7, 4)]`


If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______


If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______


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 = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.


If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1 


Choose the correct alternative:

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


If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.


Solve by matrix inversion method:

2x + 3y – 5 = 0; x – 2y + 1 = 0.


Solve by matrix inversion method:

2x – z = 0; 5x + y = 4; y + 3z = 5


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

The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?


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


If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A−1 = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.


If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.


If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______ 


If A is non-singular matrix and (A + l)(A - l) = 0 then A + A-1 = ______.


If ω is a complex cube root of unity and A = `[(ω,0,0),(0,ω^2,0),(0,0,1)]` then A-1 = ?


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


The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.


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


If matrix P = `[(0, -tan (θ//2)),(tanθ//2, 0)]`, then find (I – P) `[(cosθ, -sinθ),(sinθ, cosθ)]`


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


The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.


If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B–1 A–1)–1 is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×