Please follow these instructions carefully, as failure to fo…
Please follow these instructions carefully, as failure to follow them will result in a penalty. (i) Download the Exam template from the class website and use that to write your solutions. (ii) The solutions to each problem should be in the space specially assigned to them. (iii) When scanning your solutions into a pdf file, each page must be scanned as a separate page and the entire exam as one pdf file. (iv) You have 135 minutes to complete the exam, including the time to scan the exam and upload it as a pdf file to Proctorio I. Find all solutions to the system of equations x_1+ 3x_2+x_3+x_4=3 2x_1-2x_2+x_3+2x_4=8 3x_1+x_2+2x_3-x_4=-1 (20 points) II. Let A denote the coefficient matrix for the system of equations given in I. i) Find a basis for the Column space of A. (10 points) ii) Find a basis for the Row space of (5 points) iii) Find a basis for the Null space of A (10 points) iv) What is the rank of A? What is the nullity of A? (5 points) III. Solve the matrix equation A.x=b, where A= , x= and b= by first finding the inverse of the matrix A.(25 points) IV. Write the matrix A in III as a product of elementary matrices. (25 points)