English

State whether the following is True or False : A = [21105] is invertible matrix. - Mathematics and Statistics

Advertisements
Advertisements

Question

State whether the following is True or False :

A = `[(2, 1),(10, 5)]` is invertible matrix.

Options

  • True

  • False

MCQ
True or False

Solution

A = `|(2, 1),(10, 5)|` 
= 10 – 10
= 0
False.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Matrices - Miscellaneous Exercise 2 [Page 83]

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the inverse of the following matrix.

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


Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.


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

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


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


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

For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals


Find the inverse of the following matrices by transformation method:

`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`


Find matrix X, if AX = B, where A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "and B" = [(1),(2),(3)]`.


Fill in the blank :

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


Fill in the blank :

(AT)T = _______


State whether the following is True or False :

Singleton matrix is only row matrix.


Check whether the following matrices are invertible or not:

`[(1, 1),(1, 1)]`


Check whether the following matrices are invertible or not:

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


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)]`


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


A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1 


If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`


If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'


If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).


State whether the following statement is True or False:

Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`


If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)


Solve by matrix inversion method:

2x – z = 0; 5x + y = 4; y + 3z = 5


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

If A and B non-singular matrix then, which of the following is incorrect?


If A is an invertible matrix of order 2 then det (A-1) be equal


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


If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.


If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______ 


If AB = I and B = AT, then _______.


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


If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.


If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.


If A = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.


If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×