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  • Solve it, For two 3 × 3 matrices A and B, let A + B = 2B' and 3A + 2B = I3, where B' is the transpose of B and I3 is 3 × 3 identity matrix. Then :

For two 3 × 3 matrices A and B, let A + B = 2B' and 3A + 2B = I3, where B' is the transpose of B and I3 is 3 × 3 identity matrix.  Then :

  • Option 1)

    5A + 10B = 2I3

  • Option 2)

    10A + 5B = 3I3

  • Option 3)

    B + 2A = I3

  • Option 4)

    3A + 6B = 2I3

     

 

Answers (2)

best_answer

As we have learned

Property of Transpose -

\left ( A+B \right ){}'= A{}'+B{}'

- wherein

A and B being conformable matrices and A{}' is transpose of A

 

 We have  

A + B = 2B' .............(1)

A' + B' = 2B ...........(2) 

Also 3A +2B = I_3

   3A'  +  2B' = I_3....(3)

from 1 and 3   \rightarrow   A + B = I_3-3A'..........(4)

from 2 and 3 \rightarrow A' = I_3- 4B ...........(5)

from 4 and 5 \rightarrow A+B= I_3-3 (I_3-4B)

\Rightarrow A+B=-2I_3-12B

\Rightarrow11B-A = 2I_{3}..............(6)

now we have , 

3A+2B = I_3

11B -A = 2I_3

On solving , 

35B = 7 I_3 

B = I_3/5 

and 
A = I_3 /5

 

 

 


Option 1)

5A + 10B = 2I3

Option 2)

10A + 5B = 3I3

Option 3)

B + 2A = I3

Option 4)

3A + 6B = 2I3

 

Posted by

gaurav

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