Factor the matrix into the form QR where Q is orthogonal and R is upper triangular.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\begin{bmatrix}

a & b\\

c & d

\end{bmatrix}*\begin{bmatrix}

e & f\\

0 & g

\end{bmatrix}=\begin{bmatrix}

-1 & 3\\

1 & 5

\end{bmatrix}[/tex]

[tex]\begin{bmatrix}

a & c

\end{bmatrix}*\begin{bmatrix}

b\\

d

\end{bmatrix}=0[/tex]

[tex]ae=-1[/tex]

[tex]af+bg=3[/tex]

[tex]ce=1[/tex]

[tex]cf+dg=5[/tex]

Skipping some steps but I arrive at:[tex]\begin{bmatrix}

1 & \frac{4}{g}\\

-1 & \frac{4}{g}

\end{bmatrix}*\begin{bmatrix}

-1 & -1\\

0 & g

\end{bmatrix}=\begin{bmatrix}

-1 & 3\\

1 & 5

\end{bmatrix}[/tex]

So as long as [tex]g \neq 0[/tex] it is all good?

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# Homework Help: Factor the matrix into the form QR where Q is orthogonal

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