need solution for #2 using matlab codes to prove they live in R5

Computer Project: Subspaces Name Purpose: to deepen your understanding of span, basis and dimension. In particular, to understand what is required for two subspaces of R", which have the same dimension, to be the same sets. Prerequisite: Section 2.9 MATLAB functions that may be useful: rank, rref, diary, submats Remarks: Your instructor will supply a pair of matrices A and B, each having five rows. (There are such pairs in the file submats, and you may be assigned one of those.) Question 1 is easy, but you will need to think how to answer question 2. Discuss it with each other - this can really help. Once you figure out a method it will not take long to do the calculations. Observe that Col A and Col B are obviously subspaces of R. Directions: Use the matrices A and B which your instructor supplies. Employ MATLAB to do whatever calculations you need and attach the results. Explain your methods briefly and why they work. No credit unless your methods and explanation are valid! One way to record your work is to just copy the key calculations by hand. An easier way is to create a diary file of your MATLAB session and print that after you finish all calculations. If you want to create a diary file, here is a way: start MATLAB and type diary c:subsp before doing any calculations. This will cause everything that appears on the screen after that to be stored in a text file called subsp on your c: drive. When your calculations are finished, type diary off (or exit MATLAB) to close the file; then use your favorite editor to print the file subsp. If you want, you can first clean up the file, add titles, etc. before printing it. 1. Verify that Col A and Col B have the same dimension. 2. Determine whether or not Col A and Col B are the same subspace of R. Explain what you calculated and why it worked Notice this is not obvious. For example, if two subspaces of R each have dimension 1, each will be a line through the origin, but they might not be the same line. If each has dimension 2, they are planes through the origin, but they might not be the same plane. In general if two subspaces of R" have the same dimension k, we can visualize each as looking like R -- but they might not be the same sets. Your job here is to figure out a way to decide if two subspaces of R", which have the same dimension, are actually the same set of points, and apply your method to the subspaces Col A and Col B. 1. You may not consult with any other students than those in your group. 2. You must use MATLAB to complete this project, although you do not have to use Lay's toolbox. 3. You may not use the MATLAB function colspace. The only MATLAB functions you are allowed to use are: rank and rref. The two matrices I would like you to analyze are given below. You can copy and paste each one as it's written below into the MATLAB command line to define the matrices in MATLAB. A = (-41,-68,12,-65; -2,-18,-4.3: -86,-120,32,-94; 11,22,0,22; -3,-4,0,-3]; B = (-4,4,-4,5,-4; 7,5,-5,-2,2; -2,8,-8,8,0; 3,-1,1,-1,2; -1,0,0,0,0]; Computer Project: Subspaces Name Purpose: to deepen your understanding of span, basis and dimension. In particular, to understand what is required for two subspaces of R", which have the same dimension, to be the same sets. Prerequisite: Section 2.9 MATLAB functions that may be useful: rank, rref, diary, submats Remarks: Your instructor will supply a pair of matrices A and B, each having five rows. (There are such pairs in the file submats, and you may be assigned one of those.) Question 1 is easy, but you will need to think how to answer question 2. Discuss it with each other - this can really help. Once you figure out a method it will not take long to do the calculations. Observe that Col A and Col B are obviously subspaces of R. Directions: Use the matrices A and B which your instructor supplies. Employ MATLAB to do whatever calculations you need and attach the results. Explain your methods briefly and why they work. No credit unless your methods and explanation are valid! One way to record your work is to just copy the key calculations by hand. An easier way is to create a diary file of your MATLAB session and print that after you finish all calculations. If you want to create a diary file, here is a way: start MATLAB and type diary c:subsp before doing any calculations. This will cause everything that appears on the screen after that to be stored in a text file called subsp on your c: drive. When your calculations are finished, type diary off (or exit MATLAB) to close the file; then use your favorite editor to print the file subsp. If you want, you can first clean up the file, add titles, etc. before printing it. 1. Verify that Col A and Col B have the same dimension. 2. Determine whether or not Col A and Col B are the same subspace of R. Explain what you calculated and why it worked Notice this is not obvious. For example, if two subspaces of R each have dimension 1, each will be a line through the origin, but they might not be the same line. If each has dimension 2, they are planes through the origin, but they might not be the same plane. In general if two subspaces of R" have the same dimension k, we can visualize each as looking like R -- but they might not be the same sets. Your job here is to figure out a way to decide if two subspaces of R", which have the same dimension, are actually the same set of points, and apply your method to the subspaces Col A and Col B. 1. You may not consult with any other students than those in your group. 2. You must use MATLAB to complete this project, although you do not have to use Lay's toolbox. 3. You may not use the MATLAB function colspace. The only MATLAB functions you are allowed to use are: rank and rref. The two matrices I would like you to analyze are given below. You can copy and paste each one as it's written below into the MATLAB command line to define the matrices in MATLAB. A = (-41,-68,12,-65; -2,-18,-4.3: -86,-120,32,-94; 11,22,0,22; -3,-4,0,-3]; B = (-4,4,-4,5,-4; 7,5,-5,-2,2; -2,8,-8,8,0; 3,-1,1,-1,2; -1,0,0,0,0]