English

If A is a 3 × 3 matrix |3A| = k|A|, then write the value of k. - Mathematics

Advertisements
Advertisements

Questions

If A is a 3 × 3 matrix |3A| = k|A|, then write the value of k.

If A is a 3 × 3 matrix,

\[\left| A \right| \neq 0 \text { and } \left| 3A \right| = k\left| A \right|\] then write the value of k.

Solution

|3 A | = k |A|

|3 A | = 27|A|

k = 27

shaalaa.com
  Is there an error in this question or solution?
2015-2016 (March) All India Set 1 N

RELATED QUESTIONS

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.


In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`

The order of the matrix


In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`

Write the number of elements,


In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]` 

Write the elements a13, a21, a33, a24, a23


If a matrix has 24 elements, what are the possible order it can have? What, if it has 13 elements?


If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?


Construct a 2 × 2 matrix, `A= [a_(ij)]`, whose elements are given by  `a_(ij) = i/j`


Construct a 2 × 2 matrix, `A = [a_(ij)]`  whose elements are given by `a_(ij) = (1 + 2j)^2/2`


The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is ______.


If A, B are symmetric matrices of same order, then AB − BA is a ______.


Find matrix A such that `((2,-1),(1,0),(-3,4))A = ((-1, -8),(1, -2),(9,22))`


The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?


Write the number of all possible matrices of order 2 x 3  with each entry 1 or 2.


If `[(2x, 3)] [(1, 2),(-3, 0)] [(x),(8)]` = 0, find the valof x.


In the matrix A = `[("a", 1, x),(2, sqrt(3), x^2 - y),(0, 5, (-2)/5)]`, write: The order of the matrix A


Construct a2 × 2 matrix where aij = `("i" - 2"j")^2/2`


Construct a2 × 2 matrix where aij = |–2i + 3j|


If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is ______.


The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is ____________.


The order of [x y z] `[("a","h","g"),("h","b","f"),("g","f","c")] [("x"),("y"),("z")]` is ____________.


If A is a matrix of order m x n and B is a matrix such that AB’ and B'A are both defined, then the order of matrix B is ____________.


If A is an m x n matrix such that AB and BA are both defined, then B is a ____________.


Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is ____________.


Consider the following information regarding the number of men and women workers in three factories I, II and III

  MEN WORKERS WOMEN WORKERS
I 30 25
II 25 31
III 27 26

Which of the following represent the above information in the form of a 3 × 2 matrix.


If a matrix has 8 elements, what are the possible order it can have?


The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×