The following system of linear equations is called underdetermined because there are more variables than equations....

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The following system of linear equations is called underdetermined because there are more variables than equations. x2x 3x3 = 4 2x1x2 + 4x3 = -3 Similarly, the following system is overdetermined because there are more equations than variables. x1 + 3x = 5 2x1 - 2x = -3 -21 + 7x = 0 You will explore whether the number of variables and the number of equations have any bearing on the consistency of a system of linear equations. A. For underdetermined systems: Create a 2 x 1 vector bA with each entry between -7 and 7 using the same command randi Create a 2 x 3 random matrix A1 with each entry between -7 and 7 using the command randi Call LS_solution to find the solution so11 for the system A1x = bA Repeat the process above for the systems A2x = bA and A3x = bA to find so12 and so13, respectively B. Explain why (must use the concepts learned in Linear Algebra and may use the terms pivot or free variable in your explanations) you would expect most underdetermined linear systems to have infinitely many solutions. . Can an underdetermined linear system have a unique solution? Why or why not? Provide a reason using Linear Algebra. An underdetermined linear system can have no solution. Provide an example of an inconsistent underdetermined linear system. Do this by setting your example's matrix to example_A1 and vector to example_bl. C. For overdetermined systems -- repeat the same process Create a 3 x 1 vector bC with each entry between -7 and 7 using the same command randi Create a 3 x 2 random matrix A4 with each entry between -7 and 7 using the command randi Call LS_solution to find the solution so14 for the system A4x = bC Repeat the process above for the systems A5x=bC and A6x=bC to find so15 and 3016, respectively D. Explain why (must use the concepts learned in Linear Algebra and may use the terms pivot or free variable in your explanations) you would expect most overdetermined linear systems to be inconsistent. An overdetermined linear system can have one solution. Provide an example of an overdetermined linear system with one solution. Do this by setting your example's matrix to example_A2 and vector to example_b2. An overdetermined linear system can also have infinitely many solutions. Provide an example of an overdetermined linear system with infinitely many solutions. Do this by setting your example's matrix to example_A3 and vector to example_b3. Note: When you provide examples for Exercise 3B & 3D, they should be non-trivial examples. It means that a matrix does not contain a zero row and does not have two or more identical rows. function [name, bA, A1, Ab1, sol1, A2, Ab2, so12, A3, Ab3, so13, example_A1, example_b1, example_type1, bC, A4, Ab4, sol4, A5, Ab5, so15, A6, Ab6, so16, example_A2, example_b2, example_type2, example_A3, example_b3, example_type3] = Exercise3() % bA = --- Part A: Underdetermined Systems [10 Points] NaN; A1 = NaN; Ab1 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol1 = NaN; A2 = NaN; Ab2 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so12 = NaN; ... % A3 = NaN; Ab3 NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol3 = NaN; % Part B: Explanation of Part A [10 Points] % % (EXPLAIN) % (LEAVE THE FOLLOWING AS NaN OR PROVIDE AN EXAMPLE IF POSSIBLE) example_A1 = NaN; example_b1 = NaN; example_type1 = NaN; % (REMOVE LINE IF EXAMPLE) %[~, n] = size (example_A1); % (UNCOMMENT IF EXAMPLE) %example_type1 = LS_solution (n, example_A1, [example_A1, example_b1]); % (UNCOMMENT IF EXAMPLE) = % bC = A4 = NaN; Ab4 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol4 = NaN; Part C: Overdetermined Systems [10 Points] NaN; A5 = NaN; Ab5 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so15 = NaN; A6 = NaN; Ab6 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so16 = NaN; % --- Part D: Explanation of Part C [10 Points] % (EXPLAIN) % % The following system of linear equations is called underdetermined because there are more variables than equations. x2x 3x3 = 4 2x1x2 + 4x3 = -3 Similarly, the following system is overdetermined because there are more equations than variables. x1 + 3x = 5 2x1 - 2x = -3 -21 + 7x = 0 You will explore whether the number of variables and the number of equations have any bearing on the consistency of a system of linear equations. A. For underdetermined systems: Create a 2 x 1 vector bA with each entry between -7 and 7 using the same command randi Create a 2 x 3 random matrix A1 with each entry between -7 and 7 using the command randi Call LS_solution to find the solution so11 for the system A1x = bA Repeat the process above for the systems A2x = bA and A3x = bA to find so12 and so13, respectively B. Explain why (must use the concepts learned in Linear Algebra and may use the terms pivot or free variable in your explanations) you would expect most underdetermined linear systems to have infinitely many solutions. . Can an underdetermined linear system have a unique solution? Why or why not? Provide a reason using Linear Algebra. An underdetermined linear system can have no solution. Provide an example of an inconsistent underdetermined linear system. Do this by setting your example's matrix to example_A1 and vector to example_bl. C. For overdetermined systems -- repeat the same process Create a 3 x 1 vector bC with each entry between -7 and 7 using the same command randi Create a 3 x 2 random matrix A4 with each entry between -7 and 7 using the command randi Call LS_solution to find the solution so14 for the system A4x = bC Repeat the process above for the systems A5x=bC and A6x=bC to find so15 and 3016, respectively D. Explain why (must use the concepts learned in Linear Algebra and may use the terms pivot or free variable in your explanations) you would expect most overdetermined linear systems to be inconsistent. An overdetermined linear system can have one solution. Provide an example of an overdetermined linear system with one solution. Do this by setting your example's matrix to example_A2 and vector to example_b2. An overdetermined linear system can also have infinitely many solutions. Provide an example of an overdetermined linear system with infinitely many solutions. Do this by setting your example's matrix to example_A3 and vector to example_b3. Note: When you provide examples for Exercise 3B & 3D, they should be non-trivial examples. It means that a matrix does not contain a zero row and does not have two or more identical rows. function [name, bA, A1, Ab1, sol1, A2, Ab2, so12, A3, Ab3, so13, example_A1, example_b1, example_type1, bC, A4, Ab4, sol4, A5, Ab5, so15, A6, Ab6, so16, example_A2, example_b2, example_type2, example_A3, example_b3, example_type3] = Exercise3() % bA = --- Part A: Underdetermined Systems [10 Points] NaN; A1 = NaN; Ab1 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol1 = NaN; A2 = NaN; Ab2 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so12 = NaN; ... % A3 = NaN; Ab3 NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol3 = NaN; % Part B: Explanation of Part A [10 Points] % % (EXPLAIN) % (LEAVE THE FOLLOWING AS NaN OR PROVIDE AN EXAMPLE IF POSSIBLE) example_A1 = NaN; example_b1 = NaN; example_type1 = NaN; % (REMOVE LINE IF EXAMPLE) %[~, n] = size (example_A1); % (UNCOMMENT IF EXAMPLE) %example_type1 = LS_solution (n, example_A1, [example_A1, example_b1]); % (UNCOMMENT IF EXAMPLE) = % bC = A4 = NaN; Ab4 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) sol4 = NaN; Part C: Overdetermined Systems [10 Points] NaN; A5 = NaN; Ab5 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so15 = NaN; A6 = NaN; Ab6 = NaN; %[~, n] = NaN; % (UNCOMMENT LINE) so16 = NaN; % --- Part D: Explanation of Part C [10 Points] % (EXPLAIN) % %