For each of the following linear systems of equations

a. Showing your work, identify the complete solution set in vector form for the homogenous system, and

b. Find a particular solution for the Non-homogenous system and then find the complete solution for the non-homogenous system.

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6 7 x₁ + 3x₂ + 2x3 = 0 x₁ + x₂ + x3 + x4 = 0 0x₁ + x2 + 2x3 + 3x4 = 0 0x₁ + 0x₂ + 3x3 + 4x4 = 0 X₁ + 3x₂ + 2x3 = 10 x₁ + x₂ + x3 + x4 = 9 0x₁ + x₂ + 2x3 + 3x4 = 8 0x₁ + 0x₂ + 3x3 + 4x4 <= 10 6 7 x₁ + 3x₂ + 2x3 = 0 x₁ + x₂ + x3 + x4 = 0 0x₁ + x2 + 2x3 + 3x4 = 0 0x₁ + 0x₂ + 3x3 + 4x4 = 0 X₁ + 3x₂ + 2x3 = 10 x₁ + x₂ + x3 + x4 = 9 0x₁ + x₂ + 2x3 + 3x4 = 8 0x₁ + 0x₂ + 3x3 + 4x4 <= 10