Solving a Matrix Problem: Help Appreciated!

[JasonRox]

I'm studying for a test and I got stuck here.

Let A be the matrix:

3..1
2..1

In each part find p(a).

a) p(x)=x-2

The answer is:

1..1
2..-1

The only way I can see this happen is that we take the numbers on the diagonal and pluck it in p(x).

So...
x-2=3-2=1

x-2=1-2=-1

Leaving the others alone, we get.

1..1
2..-1


The problem is, I know this is WRONG. This method does not work for b) and c), which are polynomials of higher degrees.

The inverse is:

1..-1
-2..3

I still can see a solution pattern.

I tried to relate to the chapter, but no luck.

Any help is appreciated.

 

[Muzza]

A matrix minus a scalar? That doesn't make any sense.

 

[matt grime]

It is a matrix minus a scalar multiple of the identity matrix.

 

[JasonRox]

Let's say I choose 2x-2.

Would that be...

4..1
2..0

If this is correct, would x^2 imply multiplying both matrixes.

 

[TenaliRaman]

first of all do follow the standard notations ...
we usually use capitals for matrices ...
secondly
2X - 2
more often than not implies
2X-2I
where I is the identity matrix ...
so u can see why the answer is the way it is ...

and yes X^2 implies multiplication of matrices ... i.e X*X

-- AI

 

[JasonRox]

That's not what it says.

The question doesn't have capitals and refers to the matrix as A.

 

[TenaliRaman]

jason,
it also asks u to find p(a)
now this is really bad use of the notation actually.

p(x) =x-2 is fine
but i would expect them say
find p(A) and not p(a)

and yes when u sub in a matrix for x in an equation (in x) .. the constant (say c) is dealt as c*I ..

-- AI

 

[JasonRox]

I really appreciate your help.

I understand where you are coming from. This might be the reason why I didn't know what was going on.