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I was asked to find the LU decomposition of

$$\begin{bmatrix}5&4\\-2&-3\\\end{bmatrix}$$

I know that the shortcut method means finding the upper and using the multiplier to find the lower. In this case, you cannot multiply by one number, but you need to multiply both row one and row two. Does this mean I cannot use this method? What would be the suggested method for finding the LU decomposition?

Rodrigo de Azevedo
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Burt
  • 1,813
  • @Moo Thank you. Yes and no - I am not familiar with those methods, but they did show me that other methods exist and through them it is possible to solve a problem like this. – Burt Aug 11 '20 at 17:28

1 Answers1

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Hint:

By Gaussian elimination,

$$\begin{bmatrix}5&4\\-2&-3\end{bmatrix}\stackrel{\times\frac15}\to\begin{bmatrix}1&\frac45\\-2&-3\end{bmatrix}\to\begin{bmatrix}1&\frac45\\0&-\frac75\end{bmatrix}\stackrel{\times-\frac75}\to\begin{bmatrix}1&\frac45\\0&1\end{bmatrix}.$$

This contains all the coefficients of the LU decompostion.