QR Decomposition of Matrix: Solve for Answers

[g.lemaitre]

Homework Statement

Decompose the following matrix using QR decomposition
\begin{bmatrix}
4 & 1 \\
3 & -1
\end{bmatrix}
the answer is
\begin{bmatrix}
.8 & .6 \\
.6 & .8
\end{bmatrix}
The following matrix is supposed to be next to the previous but I can't figure out how to do that. Any help in that area would be appreciated.
\begin{bmatrix}
5 & .2 \\
0 & 1.4
\end{bmatrix}

Homework Equations

c_2 = (v_2 * u_1)q_1 + \parallel w_2 \parallel q_2

The Attempt at a Solution

I was able to get the first part of the answer
\begin{bmatrix}
.8 & \\
.6 &
\end{bmatrix}
It's the second part
\begin{bmatrix}
.6 & \\
-.8 &
\end{bmatrix}
that I'm having trouble with. I'm also not worried about the R part right now.
Ok, let's plug the numbers into this equation:
c_2 = (v_2 * u_1)q_1 + \parallel w_2 \parallel q_2
v_2 * u_1 = .2
c_2 = \begin{bmatrix}<br /> 1 &amp; \\<br /> -1 &amp;<br /> \end{bmatrix}<br />
\parallel w_2 \parallel = -49/25
Therefore,
\begin{bmatrix}<br /> 1 &amp; \\<br /> -1 &amp;<br /> \end{bmatrix} = .2 \begin{bmatrix}<br /> .8 &amp; \\<br /> .6 &amp;<br /> \end{bmatrix} - 49/25q_2
step two
\begin{bmatrix}<br /> 1 &amp; \\<br /> -1 &amp;<br /> \end{bmatrix} = \begin{bmatrix}<br /> 4/25 &amp; \\<br /> 3/25 &amp;<br /> \end{bmatrix} - 49/25q_2
step three
<br /> \begin{bmatrix}<br /> (25-4)/25 &amp; \\<br /> (-25-3)/25 &amp;<br /> \end{bmatrix} = 49/25q_2
step four
<br /> \begin{bmatrix}<br /> 21/49 &amp; \\<br /> -28/49 &amp;<br /> \end{bmatrix} = q_2
The answer is supposed to be
<br /> \begin{bmatrix}<br /> .6 &amp; \\<br /> -.8 &amp;<br /> \end{bmatrix} = q_2<br />
So I made an error somewhere.

 

[fzero]

It's tough to follow because you haven't defined every symbol, but $q_2$ should have unit norm. If you properly normalize your result, you'll find that it agrees with the solution.

 

[g.lemaitre]

It's tough to follow because you haven't defined every symbol, but $q_2$ should have unit norm. If you properly normalize your result, you'll find that it agrees with the solution.

what do you mean by properly normalize.

 

[who_]

To normalize a vector q is to find q / ||q||. Bascially, it means to scale the vector so that it lies on the unit sphere.

 

[g.lemaitre]

amazing it worked! i was skeptical that it would but it did!