Find the vector form of the general solution of the given linear system Ax = b ; then use that result to find the vector form of the general solution of Ax = 0. + x2 + 2x3 + X3 -2 2x1 + x2 + 3x3 4 O The general solution of Ax = b is (x1, x2, x3) = (– 2, 8, 0) + s( – 1, – 1, 1); and the general solution of Ax = 0 is (x1, X2, x3) = s(– 1, – 1, 1). O The general solution of Ax = b is (x1, x2, x3) = (- 2, 8, 0) + s( – 1, - 1, 1); and thejẩjneral ẩjolution ofjẩ = 0 isẩ(X1, X2, X3) = (- 2, 8, 0). O The general solution of Ax = b is (x1, X2, x3) = s(- 2, 8, 0) + (- 1, - 1, 1); and the general solution of Ax = 0 is (x|, x2, x3) = s(- 2, 8, 0). O The general solution of Ax = b is(x1, x2, x3) = s(- 1, - 1, 1); and the general solution of Ax = 0 is (x1, x2, x3) = (– 2, 8, 0) + s( – 1, – 1, 1). O The general solution of Ax b is (x1,x2, x3) = s(- 2, 8, 0) + (- 1, - 1, 1); and the general solution of Ax = 0 is (x1, X2, x3) = s(- 1, - 1, 1).

Question 1 (a) (1) What is the difference between clc and clf commands? (2) What is the purpose of using the colon (:) in matrix subscripts? (3) Having two vectors a and b, what is the difference between a / b and a ./b? (4) What is the difference between x = [-1; 0; 5] and y = [-1 0 5]? (5) Which of the following is wrong command? >> Y=3; >> *Ya= i; >>HE is = 6; >>1ST = 3. State the reason for your answers. (6) Given z = [2 i 2; i i 2i; 0 1 i], without using MATALB, what will be the type and the size of the matrix q, where q=z*inv(z)? (7) Given baby = [b a by], babyT = [b; a; b; y], case_1=baby*babyT, and case_2 = babyT*baby. Is case_1 = case_2? State the reason of your answer? (8) What is the purpose of the fprintf function in Matlab? (9) Distinguish between the array division and the matrix division. (10) What is the purpose of docking a window in Matlab? (b) Develop a Matlab function to compute the sum of even numbers of 200≤x≤1000. Call the function from the Matlab command window…

c. Lineal algebra problem  please provide a correct and well explained solution

A rectangle is inscribed in a triangle as shown. Let x denote the base of the rectangle and let y denote the height of the rectangle. Express the area A of the rectangle in terms of x and y. A = Express the area A of the rectangle in terms of x. A = (0,6) (x,y) (0,0) (6,0) Find the dimensions x and y of the inscribed rectangle with the largest area. X = y =