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Relations And Functions

Question
CBSEENMA12032420
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Construct a 3 x 4 matrix, whose elements are given by :

straight a subscript straight i space straight j end subscript equals 1 half space vertical line space minus 3 space straight i space plus space straight j right square bracket

Solution
Let A = [ai j ] be required 3x4 matrix where aij-= 2 i – j
therefore space space space straight a subscript 11 equals 2 minus 1 equals 1 comma space straight a subscript 12 equals 2 minus 2 equals 0. space straight a subscript 13 equals 2 minus 3 equals negative 1 space space space space space space straight a subscript 14 equals 2 minus 4 equals negative 2 space space space space space space straight a subscript 21 equals 4 minus 1 equals 3. space space straight a subscript 22 equals 4 minus 2 equals 2. space straight a subscript 23 equals 4 minus 3 equals 1 space space space space space space straight a subscript 24 equals 4 minus 4 equals 0 space space space space space space straight a subscript 31 equals 6 minus 1 equals 5. space space straight a subscript 32 equals 6 minus 2 equals 4. space straight a subscript 33 equals 6 minus 3 equals 3. space space space space space space straight a subscript 34 equals 6 minus 4 equals 2 therefore space space space space straight A equals open square brackets table row 1 0 cell negative 1 end cell cell negative 2 end cell row 3 2 1 0 row 5 4 3 2 end table close square brackets

Some More Questions From Relations and Functions Chapter

If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

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

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

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

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.

Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.

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