Algebraic manipulation of identity matrix

  • Thread starter KataKoniK
  • Start date
I was doing a few practice questions and was a bit confused about how the solution manual manipulated the I identity matrix. For example,

Just say you had the following

I - 2A = B

where A and B are 2x2 matrices. B is given, but we need to find A.

Therefore, shouldn't it be

-2A = B - I
A = -(1/2) * (B - I)?

Because the book did it like this

2A = I - B
A = (1/2) * (1 - B)

Can anyone tell me why? Because both statements do not seem to be equivalent. (unless I'm missing something)

Thanks in advance.
I think you may have had one of those brain lapses that I hate so much. The statements are equivalent, as the negative sign will distribute.

-(1/2)*(B-I) = (1/2)*-(B-I) = (1/2)*(I-B)
Argh, thanks a bunch. So it's just basic algebraic manipulations correct? No special things I have to do to bring I to the other side?
Nope, nothing special. Matrix addition and scalar multiplication satisfy all of the properties of regular addition and multiplication (commutativity, associativity, distributivity, etc.), so basic manipulations will suffice.
Thanks a lot!

Want to reply to this thread?

"Algebraic manipulation of identity matrix" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads