- #1

pyroknife

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## Homework Statement

$$\begin{bmatrix}

a_{11} & a_{12} & 0 & 0\\

a_{12} & a_{22} & a_{23} & 0\\

0 & a_{23} & a_{33} & a_{34} \\

0 & 0 & a_{34} & a_{44} \\

\end{bmatrix}

=

\begin{bmatrix}

q_{11} & q_{12} & q_{13} & q_{14} \\

q_{21} & q_{22} & q_{23} & q_{24} \\

q_{31} & q_{32} & q_{33} & q_{34} \\

q_{41} & q_{42} & q_{43} & q_{44} \\

\end{bmatrix}

\begin{bmatrix}

r_{11} & r_{12} & r_{13} & r_{14} \\

0 & r_{22} & r_{23} & r_{24} \\

0 & 0 & r_{33} & r_{34} \\

0 & 0 & 0 & r_{44} \\

\end{bmatrix}

$$

For the given 4x4 symmetric tridiagonal matrix A, determine which elements of its QR factorization is zero. The trick is to determine this visually.

## Homework Equations

## The Attempt at a Solution

I plugged a simple 4x4 symmetric tridagonal matrix into MATLAB and took its qr factorization and found that the top left element, ##r_{14}## of the matrix R and the bottom left 3 elements, ##q_{31}, q_{41}, q_{42}## of the matrix Q are zero. But the task was to determine this with ease and visually. Is there a trick to do this? I am not seeing it.