Consider the following statements and decide whether they are TRUE of FALSE. If a statement is false,

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

This assignment is worth 5% of your total mark.

You may use R for this assignment, but only for matrix calculations and plotting the data. If you do, include your R commands and output.

 

 

1. (3 pt) Consider the following statements and decide whether they are TRUE of FALSE. If a statement is false, provide a counterexample.

• Every nonsingular matrix is of full rank

• Every nonsingular matrix is orthogonal

• Every matrix of full rank is orthogonal

2. (4 pt) Prove that a (real) symmetric matrix A positive definite if and only if all of its eigenvalues are strictly positive.

3. (6 pt) Let y be a 3-dimensional multivariate normal random vector with mean and variance

 

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