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Let A be the set of all 3xx3 symmetric m...

Let A be the set of all `3xx3` symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0.
The number of matrices in A is

A

12

B

6

C

9

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
A symmetric matrix is symmetric about its diagonal. So, there are even number of 1 and even number of 0 as off diagonal entries. Consequently, there can be either three 1 in the diagonal or one 1 and two zeros. Thus, we have the following cases:
CASE I When diagonal elements are 1,1,1.
In this case, we have
Number of symmetric matrices
= Number of arrangements of 1,0,0 as elements above the diagonal
`=(3!)/(2!)=3`
CASE II When diagonal elements are 1,0,0 ltbr. In this case, we have ltbRgt Number of symmetric matrices
=(Number of arrangements of 1,0,0 as entries above the diagonal)
`=(3!)/(2!)xx(3!)/(2!)=9`
`:. " Total number of matrices in " A=3+9=12`
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Chapter Test
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  5. The inverse of the matrix {:[(1,3),(3,10)]:} is equal to

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  6. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  7. If {:X=[(3,-4),(1,-1)]:}, the value of X^n is equal to

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  8. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  9. For the system of equations: x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

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  10. If {:A=[(3,1),(-1,2)]:}," then "A^(2)=

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  11. if A=[(4,x+2),(2x-3,x+1)] is symmetric, then x is equal to

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  12. If A+B={:[(1,0),(1,1)]:}andA-2B={:[(-1,1),(0,-1)]:}, then A is equal t...

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  13. {:[(-6,5),(-7,6)]^(-1)=:}

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  14. From the matrix equation AB=AC, we conclude B=C provided.

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  15. If I3 is the identily matrix of order 3, then (I3)^(-1)=

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  16. Let a ,b , c be real numbers. The following system of equations in x ,...

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  17. If A and B are two matrices such that A+B and AB are both defind, then

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  18. A and B are tow square matrices of same order and A' denotes the tran...

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  19. STATEMENT-1: The lines a(1)x+b(1)y+c(1)=0a(2)x+b(2)y+c(2)=0,a(3)x+b(3)...

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  21. If A and B ar square matrices of order 3 such that |A|=-1|B|=3, then |...

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