हिंदी

For the matrix A = (2,3),(5,7), find (A + A') and verify that it is a symmetric matrix. - Mathematics

Advertisements
Advertisements

प्रश्न

For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.

योग

उत्तर

`"A" = [(2,3),(5,7)]`

`"A+A"\prime = [(2,3),(5,7)] + [(2,5),(3,7)] = [(4,8),(8,14)]`

`("A+A"\prime)""^\prime= [(4,8),(8,14)] = ("A+A"\prime)`

Thus, `("A + A"\prime)` is a symmetric matrix.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2018-2019 (March) 65/4/3

संबंधित प्रश्न

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.


Show that each of the relation R in the set A= {x  ∈ Z : 0 ≤ x  ≤ = 12} given by R = {(a, b) : |a - b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1 in each case.


Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.


Given a non-empty set X, consider P (X), which is the set of all subsets of X. Define the relation R in P(X) as follows:

For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.


Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is

(A) 1

(B) 2

(C) 3

(D) 4


Test whether the following relation R2 is (i) reflexive (ii) symmetric and (iii) transitive:

R2 on Z defined by (a, b) ∈ R2 ⇔ |a – b| ≤ 5


Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R2 = {(2, 2), (3, 1), (1, 3)}, R3 = {(1, 3), (3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is (i) reflexive (ii) symmetric (iii) transitive.


Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.


Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.


Let Z be the set of all integers and Z0 be the set of all non-zero integers. Let a relation R on Z × Z0be defined as (a, b) R (c, d) ⇔ ad = bc for all (a, b), (c, d) ∈ Z × Z0,
Prove that R is an equivalence relation on Z × Z0.


If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.


Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.


Let R be the relation over the set of all straight lines in a plane such that  l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .


Mark the correct alternative in the following question:

Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is _____________ .


If A = {a, b, c}, B = (x , y} find A × A.


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∪ C).


Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}. Is R reflexive? symmetric? transitive?


Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive


Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation


If A = {1, 2, 3, 4 }, define relations on A which have properties of being: 
symmetric but neither reflexive nor transitive


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from B to A


Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.


Which of the following is not an equivalence relation on I, the set of integers: x, y


If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.


Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is ____________.


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • The above-defined relation R is ____________.

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.


If A is a finite set consisting of n elements, then the number of reflexive relations on A is


lf A = {x ∈ z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×