This is linear algebra, I just need help with these few questions please

x + y + Zz = 1 1. [6 points] Consider the following system: J: + kz = 1 y+z=h [A] Apply the elementary row operations to the corresponding augmented matrix to the system above in order to write it in an echelon form. [solution] [3} Determine the values of k and it such that the linear system has a specific number of solutions stated in the table given below; [solution] - Many solutions 1 1 2 1 [Ci-{Mi Let A = 1 I] it be the coefcient matrix of the system with many solutions in {B} above. Suppose that u = 5 . 1 1 8 {C} Find the general solution of the system in para metric vector form. [solution] [Di Describe the solution set in [C] above geometrically [solution] [E] Is A invertible? Explain why or why not with out trying to find its inverse if there is any. [solution] [F] Find the null space of A. {solution} [G) Find the column space of A. [solution) (H) Find an orthogonal basis of the column space of A, that is not and the dimension of the column space of A. You need to show your work not using a guess, (solution) (1) Show that B s a basis of the column space of A. [solution) Find the B-coordinates or ].we.- - - J;]- 12.1- (solution) (K) Find the orthogonal projection of u = onto the column space of A. (solution) (L) Find the orthogonal complement of the column space of A. (solution) (M) Find the distance from u to the column space of A. Again, recall that you are supposed to use what you have learned in Linear Algebra, not Elementary Algebra to earn credits. [solution)