SOLUTION: True or False (justify your answer <a rel=nofollow HREF="http://www.gulfup.com/" target="_blank" title="&#1605;&#1585;&#1603;&#1586; &#1578;&#1581;&#1605;&#1610;&#1604; &#1575

Algebra.Com
Question 928086: True or False (justify your answer

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
(a)

A2B = (AA)B = A(AB) = A(BA) = (AB)A = (BA)A = B(AA) = BA2 

(b)

               A2 - 3A + I = 0

            A2 - (3I)A + I = 0

       A-1[A2 - (3I)A + I) = A-1(0)

 A-1A2 - A-1[(3I)A] + A-1I = 0

A-1(AA) - [A-1(3I)]A + A-1 = 0

A scalar multiple of the identity commutes with all other matrices.

(A-1A)A - [(3I)A-1]A + A-1 = 0

     IA - (3I)[A-1A] + A-1 = 0

           A - (3I)I + A-1 = 0

              A - 3I + A-1 = 0

                         A = 3I - A            
 
(d)



is the coefficient matrix of this system for some p,q,r:



  
 
if =4, the system is





This is inconsistent unless r=0

--------------------------

if =6, the system is





This is inconsistent unless p=0
  
Edwin
RELATED QUESTIONS

(answered by MathLover1)
(answered by TimothyLamb)
(answered by tommyt3rd)
(answered by tommyt3rd)
This question below is part 2 of a question I had recently posted on algebra.com ( please (answered by math_tutor2020,ikleyn)
Could you please help me write an INDIRECT PROOF for this problem? (answered by greenestamps,Edwin McCravy)
Please help me with this calculus problem about derivatives of Inverse functions. (answered by MathLover1,ikleyn)
(answered by mananth)
(answered by MathLover1)