Homework Help: Matrices - Composition

1. Feb 27, 2014

teme92

1. The problem statement, all variables and given/known data

a) Find the inverse of the matrix:
$$\begin{pmatrix}1 & 2 & 0\\ 2 & 0 & 1\\ 1 & 1 & 2\end{pmatrix}$$

(sorry I don't know how to show a matrix more clearly on this)

b) Write A and A-1 as a composition of matrices of the form Rij(k), Tij and D22(k)

2. Relevant equations

3. The attempt at a solution

So I've done part (a) and ended up with the inverse as:

$$\begin{pmatrix}1/7 & 4/7 & -2/7\\ 3/7 & -2/7 & 1/7\\ -2/7 & -1/7 & 4/7\end{pmatrix}$$

(sorry again)

My problem is, I don't understand part (b). Any help would be much appreciated.

Last edited: Feb 27, 2014
2. Feb 27, 2014

BvU

Code (Text):
$$\begin{pmatrix} 1 & 2 & 3 & 4\\ a & b & c & d\\ x & y & z & w \end{pmatrix}$$
yields
$$\begin{pmatrix} 1 & 2 & 3 & 4\\ a & b & c & d\\ x & y & z & w \end{pmatrix}$$

When you say "I don't understand part (b)" does that mean that you don't know what is meant with Rij(k), Tij and D22(k) ?

3. Feb 27, 2014

teme92

Hey BvU,

Thanks for showing me that, I've edited it there now so it should be easier to read. Yes, I don't understand that. I also don't understand what it means when it say wrote them as a composition. Thanks for the help again

4. Feb 27, 2014

BvU

Oops, caught with my pants down. I don't know either.
So now you will have to find out what is meant. Do you have a syllabus or a textbook ?

Composition is easy to find, though: $(T \circ S) (x) \equiv T(S(x))$

5. Feb 27, 2014

Staff: Mentor

I don't know what these are, either. Please show us how these are defined: Rij(k), Tij and D22(k).

(Shouldn't that last one be D33(k)?)

6. Feb 28, 2014

teme92

It's ok at least you tried to help :). I don't have a textbook or a particular syllabus no. I'm doing past exam questions for my Linear Algebra course and I came across this

7. Feb 28, 2014

teme92

And Mark44, its says 22 in the question.

8. Feb 28, 2014

Staff: Mentor

Without knowing what the notation means, there's no way we can help you with this problem.

We don't have enough information to determine whether D22(k) is a typo or even what it means, if it's not a typo.