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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