Home
Class 12
MATHS
A 3xx3 determinant has entries either 1 ...

A `3xx3` determinant has entries either `1` or `-1`.
Let `S_(3)=` set of all determinants which contain determinants such that product of elements of any row or any column is `-1` For example `|{:(1,,-1,,1),(1,,1,,-1),(-1,,1,,1):}|`is an element of the set `S_(3)`.
Number of elements of the set `S_(3)=`

A

`10`

B

`16`

C

`12`

D

`18`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` For `S_(n),a_(11),a_(12),a_(13),….a_(1(n-1))` we have two options `'1'` or `'-1'`m but for `a_(1n)` we have only one way depending upon the product `(a_(11)*a_(12)*a_(13)*…..*a_(1(n-1)))`
`:.` For `R_(1)` we have `2^(n-1)` ways
Similarly for `R_(2),R_(3),R_(4),....R_(n-1)` we have `2^(n-1)` ways
For `R_(n)` we have only one way.
Hence total number of ways `(2^(n-1))^(n-1)=2^((n-1)^(2))`
For `S_(3)`, we have `2^((3-1)^(2))=1` elements.
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Single correct Answer|42 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DETERMINANTS

    CENGAGE|Exercise Question Bank|23 Videos

Similar Questions

Explore conceptually related problems

If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

A determinant is chosen at random from the set of all determinants of order two with elements 0 or 1 only. Probability that the determinant chosen has positive value is

Find minor or element 5 in the determinant Delta=|{:(2,4,3),(1,5,2),(-1,4,1):}|

Let S={1,2,3,.....50} The number of non empty subsets A of S such that the product of elements is A is even

The cofactor of the element '4' in the determinant |(1,3,5,1),(2,3,4,2),(8,0,1,1),(0,2,1,1)| is

Multiply the following determinants and obtain four different determinants by multiplying row to row, to column , column to row and column to column |{:(3,4),(1,2):}|xx|{:(6,2),(3,1):}|

Let S={1,2,3,......,100}. The number of non-empty subsets A of S such that the product of elements in A is even is

Write minors and cofactors of the elements of the determinants: |{:(1,0,4),(3,5,-1),(0,1,2):}|

Let A be the set of all 3xx3 matrices of whose entries are either 0 or 1. The number of elements is set A, is