4.4.17 Find a basis for the solution space of the given homogeneous linear system. X1 - 3x2 + 5x3 - 5x4 = 0 2x1 5x2 + 12x3 - 5x4 = 0 A basis for the solution space of the given homogeneous linear system is (Use a comma to separate vectors as needed.)

Find a basis for the solution space of the given homogeneous linear system. X₁ 3x2 5x4 = 0 - 9x3 2x₁ + 2x₂ - 2x3 + 14x4 = 0 X₁ + 6x₂ + 9x3 + 22x4 = 0 A basis for the solution space of the given homogeneous linear system is 1. (Use a comma to separate vectors as needed.)

Find a basis for the solution space of the given homogeneous linear system. X₁ + 5x₂ + 13x3 + 14x4 = 0 2x₁ + 6x₂ + 14x3 + 15x4 = 0 2x₁ + 8x₂ + 20x3 + 22×4 = 0 A basis for the solution space of the given homogeneous linear system is (Use a comma to separate vectors as needed.)

Solve a linear system to determine whether the given vectors u, v, and w are linearly independent. or dependent. If they are linearly dependent, find scalars a, b, and c not all zero such that au+by+ cw =0. -3 u= = W= @ @ @ W-[:] A) The vectors u, v, and w are linearly independent. OR B) The vectors u, v, where a= the value of 1 c is (please Simplify your answer) linearly dependent, and C=1, where choosen to be equal to 1. and w b= are

Find the solution vectors u and v such that the solution space is the set of all linear combinations of the form su + tv. X₁ - 3 x₂ + x3 - 11x4 = 0 + 19 X4 x2 + x3 + 13x4 X₁ + 2x₂ + x3 x₁ + The solution vectors are u = = 0 = 0 and v= such that x = su + tv, x3 = s and x4 = t, where s and t are real numbers.

Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for the dimension and in any cell of the vector.) 2x₁ + 4x₂ - 4x3 + 2x4 = 18 3x₁2x₂ + 2x3 - 5x4 = 35 4X₁ + X₂ X3 + 4x4 1 dimension basis ↓↑