The total number of 3 xx 3 matrices A ...

The total number of `3 xx 3 ` matrices A having entries from the set `{0,1,2,3}` such that the sum of all the diagonal entries ` A ^(T)A` is 9, is equal to `"________"`

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The number of all 3times3 matrices A ,with entries from the set {-1,0,1} such that the sum of the diagonal elements of A A^(T) is 3 ,is k then (k)/(10) is

The number of all 3times3 matrices A ,with entries from the set {-1,0,1} such that the sum of the diagonal elements of A A^(T) is 3 ,is k then (k)/(10) is

Knowledge Check

If A=[(0,1,2),(1,2,3),(3,1,1)] , then the sum of the all the diagonal entries of A^(-1) is

A

2

B

3

C

`-3`

D

4

How many matrices X with entries {0,1,2} are there for which sum of diagonal entries of X.X^(T) is 7?

A

560

B

562

C

504

D

540

the total number of ways of selecting two number from the set {1,2,3,4,…..3n} so that their sum divisible by 3 is equal to -

A

`(2n^(2)-n)/(2)`

B

`(3n^(2)-n)/(2)`

C

`2n^(2)-n`

D

`3n^(2)-n`

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