Advertisements
Advertisements
प्रश्न
For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Determine whether the following relation is reflexive, symmetric and transitive:
Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer}.
Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.
Given an example of a relation. Which is reflexive and symmetric but not transitive.
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.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?
Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.
Defines a relation on N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Prove that the relation R on Z defined by
(a, b) ∈ R ⇔ a − b is divisible by 5
is an equivalence relation on Z.
If R is a symmetric relation on a set A, then write a relation between R and R−1.
Define a transitive relation ?
R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .
The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a2 − b2 | < 16} is given by ______________ .
If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .
If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .
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 = {1, 2, 3, ... 9} and R be the relation in A × A defined by (a, b) R(c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]
Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.
A relation R on a non – empty set A is an equivalence relation if it is ____________.
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 ____________.
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). 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 ____________.
Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.
Answer the following using the above information.
- Let relation R be defined by R = {(L1, L2): L1║L2 where L1, L2 ∈ L} then R is ____________ relation.
The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is
In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?
Let R = {(a, b): a = a2} for all, a, b ∈ N, then R salifies.
Define the relation R in the set N × N as follows:
For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.
Let R1 and R2 be two relations defined as follows :
R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and
R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q}, where Q is the set of all rational numbers. Then ______
Let R = {(x, y) : x, y ∈ N and x2 – 4xy + 3y2 = 0}, where N is the set of all natural numbers. Then the relation R is ______.
