Consider the homogeneous system of linear equations. For convenience, their general solution is given. It can...

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Consider the homogeneous system of linear equations. For convenience, their general solution is given. It can be shown that the solution of the system forms a subspace W of some R". Find a basis for the subspace of the solution and give dimension. x₁ + x₂8x3 + 10x = 0 x2 - x3 + 3x40 X₁ + 2x₂9x3 + 13x4 0 The general solution is (7r - 7s, r- 3s, r, s). basis dimension Give written description of the subspace. O a plane through the origin of R³ O a three-dimensional subspace of R³ O a line through the origin of R² O a line through the origin of R³ O a plane through the origin of Rª Consider the homogeneous system of linear equations. For convenience, their general solution is given. It can be shown that the solution of the system forms a subspace W of some R". Find a basis for the subspace of the solution and give dimension. x₁ + x₂8x3 + 10x = 0 x2 - x3 + 3x40 X₁ + 2x₂9x3 + 13x4 0 The general solution is (7r - 7s, r- 3s, r, s). basis dimension Give written description of the subspace. O a plane through the origin of R³ O a three-dimensional subspace of R³ O a line through the origin of R² O a line through the origin of R³ O a plane through the origin of Rª

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