Question 1. Consider E = {(x,y,z, t) ER¹: x = t₁y = z} a)Determine whether the given set is subvector space or not b) Show that this set is a basis for R4. c) What is the dimension of E=? Question2. In the following linear system, determine all values of a for which the resulting linear system has (a) no solution; (b) a unique solution; (c) infinitely many solutions: x + 2y + z = 1 y +z = 0 -a²x + (4-2a²)y = 2 Question3. Solve the system of equations by using LU method 2x + y + 3z = -1 6x + y +9z = 5 4x + 2y +7z = 1