Math 1104C, 1104J: Test # 1, Due Feb. 9 11:59, 2022 Directives: • This document has 2 pages (including this page). • This assignment is due on February 9th at 11:59 on Brightspace. • The assignment...

You can write all your answers on a piece of paper of your choice.


Math 1104C, 1104J: Test # 1, Due Feb. 9 11:59, 2022 Directives: • This document has 2 pages (including this page). • This assignment is due on February 9th at 11:59 on Brightspace. • The assignment has 8 questions for a total of 40 points. • You must show your work when appropriate. We look at lot more at your work than your final answer and we need to see your work when asked. IMPORTANT: Submit a scan or pictures of your work. You can write all your answers on a piece of paper of your choice or an electronic tablet or use latex. Instructions to submit your assignment online • You must send a scan or a picture of your work. It must clear enough so that we can read what you wrote. We are only marking what we receive so make sure to send complete files. • only .pdf and .jpg files are accepted. • Make sure to submit your work at the appropriate link of the exam on Brightspace. • Only the last version of a file or document that you submit is marked. • Please submit your work as only one file or folder • No late work will be accepted. You can contact me by email at [email protected]. 1 mailto:[email protected] 1. (5 points) Use Gauss-Jordan elmination to find all solutions to the linear system: x1 + 3x2 + 2x3 + 4x4 = 2 x3 + x4 = 2 2x1 + 6x2 + 3x3 + 7x4 = 2 2. (5 points) Let A = 0 1 0 1 0 00 0 1 0 1 0 1 0 0 0 0 1  ~b = 11 1  Find the reduced row echelon form of (A|~b). Use it to find a solutions to A~x = ~b. 3. (5 points) Solve the system A~x = ~0 using the matrix A from question 5. 4. (6 points) Let A = ( 1 0 −1 1 1 1 ) . Is ~b = ( 3 2 ) in the span of the columns of A? Is ~w = ( −1 1 1 ) in the span of the rows of A? 5. (6 points) Let A = ( 3 −1 2 −1 2 4 ) , B =  1 2−1 −2 0 3  , C = (0 1 1 0 ) Evaluate the following expressions if they make sense. (a) CB (b) BC (c) AB + C (d) BA + C (e) CT + C (f) B + AT 6. (3 points) Give an example of a matrix M where MMT and MTM are not equal matrices. 7. (5 points) Is P = ( 8 1 5 −2 ) a linear combination of the three matrices Q1 = ( 1 1 1 1 ) , Q2 = ( 0 1 −1 0 ) , Q3 = ( 1 0 0 −1 ) 8. (5 points) Find the inverse of the following matrix: 1 1 −10 1 1 0 1 −1  Page 2