English

If A = [6556] and B = [110011] then find A'B' - Mathematics and Statistics

Advertisements
Advertisements

Question

If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'

Sum

Solution

A'B' = `[(6, 5),(5, 6)]^' [(11, 0),(0, 11)]^'`

= `[(6, 5),(5, 6)] [(11, 0),(0, 11)]`

= `[(66 + 0, 0 + 55),(55 + 0, 0 + 66)]`

= `[(66, 55),(55, 66)]`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.2: Matrics - Short Answers I

RELATED QUESTIONS

Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`


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 co-factor of the element of the following matrix.

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


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

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


Find the inverse of the following matrix by the adjoint method.

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


Find the inverse of the following matrix.

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


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

`((1,3),(2,7))`


Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -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 the following matrices by transformation method: `[(1, 2),(2, -1)]`


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


Choose the correct alternative.

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


Fill in the blank :

(AT)T = _______


Fill in the blank :

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


Solve the following :

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


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 :

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


If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______


`cos theta [(cos theta, sin theta),(-sin theta, cos  theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______


If the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α


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


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


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


If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]`  then, show that the inverse of A is A itself.


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


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


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


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


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


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


If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is ______.


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


If matrix A = `[(1, -1),(2, 3)]`, then A2 – 4A + 5I is where I is a unit matix.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×