Inverse Matrix and Composition of Matrices: Solving Homework Problems

[teme92]

Homework Statement

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

(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 R_ij(k), T_ij and D₂₂(k)

Homework Equations

The Attempt at a Solution

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

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

(sorry again)

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

 

[BvU]

[tex]
\begin{pmatrix}
1 & 2 & 3 & 4\\
a & b & c & d\\
x & y & z & w
\end{pmatrix}
[/tex]

yields
$$\begin{pmatrix}<br /> 1 & 2 & 3 & 4\\<br /> a & b & c & d\\<br /> x & y & z & w<br /> \end{pmatrix}$$

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

 

[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

 

[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: $(T \circ S) (x) \equiv T(S(x))$

 

[Mark44]

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

(Shouldn't that last one be D₃₃(k)?)

 

[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

 

[teme92]

And Mark44, its says 22 in the question.

 

[Mark44]

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

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

And Mark44, its says 22 in the question.

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.