Constants: a = 2, b = 2 Solve the following homogeneous system: x1 + x2 + 2x3 + x4 + x5 = 0 bx1 − x2 + x3 + 2x4 + 5x5 = 0 x1 + 3x2 + 4x3 + 3x4 + 3x5 = 0

Find all basic solutions to the following homogeneous system and express the general solution as a linear combination of these basic solutions: -2x1 + 2x2 ― x34x4x5 = 0 2x12x2 + 2x3 - 2x4 = 0 2x12x2 3x3 + x5 3x3x5 = = 0

X1 = x2 = || || x3 Solve the following system of three linear equations in three unknowns. 2x₁ +6x₂ + x3 = -2 x₁ + 3x₂ = -2 4x₁ +8x₂ + x3 = -2

Find the number of real solutions (x,y) of the system of equations x³ + y² + y² = 0, x² + x²y + xy² = 0 +3