Reduce the given system to echelon form to find a single solution vector u such that the solution space is the set of all scalar multiples of u. X₁ + 7x₂ + 2x3 - 8 x4 = 0 2x₁ + 7x₂ + X3 -7 X4 = 0 X3 - 4 x4 = 0 3x₁ + 5x2 Find u. u=

Find the general solution of the simple homogeneous "system" below, which consists of a single linear equation. Give your answer as a linear combination of vectors. Let x2 and x3 be free variables. 2x1 - 8x2 + 6x3 = 0 O x2 = X₂ 0 + X3 1 (with X2, X3 free) Ox1 x2 = 4x2 x3 Ox1 x2 = X2 1 0 x3 x1 +3x2 (with x2, X3 free) x3 -3 A 1 + X3 0 (with X2, X3 free) 640-8 x2 FX2 1 + X30 (with X2, X3 free)