find the number of 2*2 matrix satisfying...

i) aij is 1 or -1

ii) (a11)2 +(a12)2 = (a21)2 + (a22)2 =2

iii) a11a21 + a12a22 =0

A 2×2 matrix is generally represented as

                     

(i) The condition is aij is 1 or – 1. i.e. each element has two choices.

Total number of elements are 4.

∴ Number of matrix satisfying the condition aij = 1 or – 1 are (2)4 = 16

 

(ii) Given condition is –

In your query, you did not mention from where the entries are taken in the matrix i.e. either      aij ∈N or  aij ∈ R.

if aij ∈ N, then

is possible only when a11 = a12 = a21 = a22 = 1.

Hence, the number of 2 × 2 matrix satisfying the condition is only one.

If aij ∈ R, then there will be infinite matrices which satisfies this condition.

 

(iii) The given condition is:

a11 a21 + a12 a22 = 0

If aij ∈ R, then this condition is satisfied by infinite values of aij.

Hence, no.of matrix satisfying condition (iii) are infinite.

If  aij ∈N, then there will be no matrix which will satisfy this condition as for natural numbers this condition can never hold..

  • -11

 i). This can be done when each of the 2 elements is selected as either 1 or 01 so no of ways = (2)4 =16

ii).infinite

iii).infinite

  • -9
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