Advanced Linear Algebra for Machine Learning Instructions: Mark the question number and your final answer clearly (use a textbox.) Remember to show and explain your work (If you can't explain it, you don't understand it.) Let = [ 0 3 1 1 4 2 1 3 1 ] = [ 2 1 2 1 0 1 1 2 2 ] = [ 2 1 4 ] = [ 2 1 5 ] = 2 = 1 (3 points) Question 1: 1) 2% - Calculate 1 + 2) 1% - Validate your answer using Python. (4 points) Question 2: 1) 3% - Using the cosine formula, and assuming the angle between vectors and is equal to , calculate cos . 2) 1% - Validate your answer using Python. (4 points) Question 3: 1) 3% - Calculate ( ) 2) 1% - Validate your answer using Python. (4 points) Question 4: 1) 3% - Let () and be the trace and lower triangular matrix of matrix , respectively. Calculate + () 2) 1% - Validate your answer using Python. Advanced Linear Algebra for Machine Learning Instructions: Mark the question number and your final answer clearly (use a textbox.) Remember to show and explain your work (If you can't explain it, you don't understand it.) (4 points) Question 1: 1) 2% - Choose a value which gives no solution. 2) 2% - Choose a value which gives infinitely many solutions. 3 + 6 = 1 6 + 12 = (6 points) Question 2: 1) 5% - Solve the following system of equations using Gaussian Elimination. 2 + 3 + = 12 2 + 3 2 = 1 + 4 = 16 2) 1% Validate your answer using Python. (4 points) Question 3: 4% - Find the rank of each of the following matrices. Verify your rank calculation using Python. a) = [ 1 0 0 0 3 0 0 0 1 2 0 0 2 1 3 3 0 3 2 1 ] b) = [ 1 1 0 1 2 2 1 4 1 1 2 3 ] (1 points) Question 4: 1% - Determine whether the following set of vectors is linearly independent or linearly dependent. a) [ 1 2 ],[ 1 1 ],[ 1 0 ]