Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3x3 = 0 -2x1 + x2 - X3 = -2 x - 3x2 + 6x3 = 3 Let x be the vector x = |x2, where x1, x2 and x3 are solutions of the system, and y be the vector y =|1. Evaluate the scalar product of x and y. [Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer. So for example, if the correct answer is 6.78 then any input that lies between between 6.53 and 7.03 will be marked as correct.] Answer:

Find the LU factorization of A 4 -20 A = 1 T2 || || 5 -26 T - 2 188 50 - L 4 -20 4² -26 and use it to solve the system 1.881

solve all 132

Describe and compare the solution sets of x₁ +5x₂ - 2x3 = 0 and x₁ + 5x₂ - 2x3 = -7. X1 E Describe the solution set, x= x₂ of x₁ +5x₂ - 2x3 = 0 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. X3 (Type an integer or fraction for each matrix element.) OA. X= O B. X=X3 C. X=X₂ O D. X= + X3 X1 E x2 of x₁ + 5x₂ - 2x3 = = -7 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. x3 (Type an integer or fraction for each matrix element.) OA. X= B. X= +X₂ Describe the solution set, x = O c. x= O D. X=X₂ +X3 +x₂ + X3 +X3 Which option best compares the two equations? O A. The solution set of the second equation is a plane perpendicular to the line that is the solution set of the first equation. O B. The solution set of the second equation is a plane parallel to the plane that is the solution set of the first equation. OC. The solution set of the second equation is a plane parallel to…

Please include easy and clear explanation for each solving step

Determine whether 2 4 are linearly independent.