2. Determine a basis for and the dimension of the solution space of the homogeneous system X3 + X4 + X5 = 0 -x1 – x2 + 2x3 – 3x4 + x5 = 0 X1 + x2 – 2x3 - X5 = 0 2х, + 2x2 — Хз + X5

2.) Use the rank criterium to find out whether the following System of linear equations has a solution : x₁ + x₂ + x3 - 2xy =0 2X₂+3x₂ = 1 3X₁ X₂ + x3 + xy = 3 4x1 +2х3 тохи = 5

9. In each part, determine whether the given 3-tuple is a solution of the linear system (a) (3, 1, 1) 2x1 - 4x₂ - x3 = X3 X₁ - 3x₂ + 3х1 — 5x2 — 3х3 (b) (3,-1, 1) x3 = = = (c) (13, 5, 2)

Find a basis for the solution space of the given homogeneous linear system. 9x3 5x4 X₁ - 3x₂ - 2X1 3x2 12x3- X4 = 0 = X₁ + 2x₂ + X3 + 10x4 0 - = 0 =