Find a basis for the solution space of the given homogeneous linear system. X₁ + 5x₂ + 13x3 + 14x4 = 0 2x₁6x₂14x3 + 15x4 2x₁ + 8x2 + 20x3 + 22x4 = 0 = 0

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x₁, x2, and x3 in terms of the parameter t.) 2x1 + 3x3 = 3 4x1 - 3x2 + 7x3 = 2 8x19x2 + 15x3 = 15 (x1, x2, x3) = |

Solve the following homogeneous system of linear equations: x1+x2+x3-2x4 = 0 -3x1-3x2+2x3-9x4 = 0 -3x1-3x2-2x3+6x4 = 0 -x1-x2-3x3+7x4 = 0 -2x1-2x2-x3-2x4 = 0 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has infinitely many solutions The system has no solution The system has a unique solution The system has infinitely many solutions x2 = 0 + s0 X3

Find A, x, and b such that Ax = b corresponds to the given linear system. (Do not perform any row operations.) -10 2x₁ + 9x₂ - 4x3 = -X₁ - 3x₂ + 8x3 = 4 A = X = b = ↓ ↑ ↓ ↑ →