**Due date: September 28**

Please email the graphics for problem 3 to me with the subject line
*stat6341 homework 1*. Problems 1 and 2 can be turned in handwritten on paper. If you
wish to include graphics in a document such as Word, please save your document as a pdf file and
email that, not the Word file.

- Show that if
*A*is a square matrix and is nonsingular, then*A*is nonsingular.**Hint**: use the SVD. - Let
*S*be an matrix with . Show that*I-S*is nonsingular and that is orthogonal.**Hint**: first show that is nonsingular. Then show and use the fact that

- The file

http://www.utdallas.edu/~ammann/stat6341scripts/OgleSMCV.csv

contains stellar magnitudes (luminosity) and log(period) for a family of variable stars called Cepheid variables in the Small Magellenic Cloud. The first column of this file gives IDs for the Cepheids and so can be used as row names. These variable stars are important to astronomers because the periods of their variability (*logPeriod*) are directly related to their luminosity. This enables astronomers to estimate distances of these stars from their periods. Two types of Cepheids are contained in this data set, FU and FO, and these types have slightly different period-luminosity relationships.**Note**: stellar magnitudes are reversed in the sense that higher value for magnitude corresponds to a dimmer star.- a.
- Construct a plot of infra-red luminosity (
*I*) vs*logPeriod*that uses different colors for the two types of Cepheids. Include an informative title and a legend that shows which color is assigned to which type. - b.
- Construct a pairs plot of
*I,V,B,logPeriod*that uses different colors for Cepheid types. Include an informative title. - c.
- Construct a graphic that show how infra-red luminosity differs between types. Repeat
for visual (
*V*), blue (*B*), and*logPeriod*.

2017-12-10