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The number of elements that a square mat...

The number of elements that a square matrix of order n has below its leading diagonal, is

A

`(n(n+1))/2`

B

`(n(n-1))/2`

C

`((n-1)(n-1))/2`

D

`((n+1)(n+1))/2`

Text Solution

Verified by Experts

The correct Answer is:
B
There `aren^2` elements in a square matrix of order n out of which n elements other than diagonal elemenets is `(n^2-n)`.
Half of these elements are above the diagonal and half are below the diagonal.
So, required number of elements is `(n^2-n)/2=1/2n(n-1)`.
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OBJECTIVE RD SHARMA-MATRICES-Chapter Test
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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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  12. If {:A+B=[(1,0),(1,1)]andA-2B=[(-1,1),(0,-1)]:}," then "A=

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

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

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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 positive real numbers. The following system of equation...

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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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  20. The system of linear equations x+y+z=2 2x+y-z=3 3x+2y+kz=4 has a...

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