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Grade 12Algebra

  • Let A & B be 3*3 matrix of real numbers , where A is symmetric & , B is skew symmetric, &(A+B)(A-B)=(A-B)(A+B).if (AB)T =(-1)k AB,where (AB)T is the transpose of the matrix AB, then the possible values of k are
    Ans=1&3

Profile image of Ayush Anurag Sawal
17 Years agoGrade 12
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1 Answer

Profile image of Pratham  Ashish
17 Years ago

hi ayush,

(A+B)(A-B)=(A-B)(A+B)

we will get AB = BA

 

use dis property to get one of d values

(AB)T = BTAT

so apply dis n write BT = -B (as dis is a skew symm)

u will get(AB)T   =(-1) AB     (AB= BA , using d given condition)

 

thus getting value of k=1