IIT JEE , AIEEE Forum - Mathematics , Algebra

sagar90

if A²+ I =0 I= identity matrix thn A^-1?

dheer_07

A INVERSE = - A

plz rate if im right

hash_include

answer:

-i 0
0 -i

where i = root(-1)

sagar90

i also knw the answer but how it came?

dheer_07

WATS THE ANS???

jeesucks

sagar90

yaar give explanation .........

sagar90

common give the soln
otherwise how ur answer came thn??

varshavallig

its simple
multiply A# in the front i.e pre multiplication.,then it will bcom
(A'A)A+A'I=0
IA+A'=0
A'=-A
hope this helps
!!!!!!!!!!!!!!!

premsharma

yeah thats right

fwks_phoenix

A²+ I =0 I= identity matrix thn A^-1? '

AA^-1=I

so

A²+I=A²+AA^-1 = 0

A(A+A^-1)=0

A cannot b equal to zero since Inverse exists

A+A^-1 =0

so A^-1 = -A

sagar90

http://www.goiit.com/posts/list/differenciation-limit-doubt-47692.htm
guys try this one (give full soln)

If A = 2 3 and A^-1 = kA thn k equals ?

5 -2

fwks_phoenix

in this case also inverse exists as det A is not equal to zero

so multiply on both sides by A

AA^-1=kAA

AA^-1=I

so kA²=I

now find A², mltiply each element by k and equate the elements to that of I..u'll get k..

19 0

0 19 this is A²

and now kA²

K19 O

0 K19

K19=1

K=1/19