Which of the following are true for matrix A in reduced row echelon form (there is no augmented column): 1 0 2 01 0 1 -2 0 2 0 0 0 1 3 The columns form a spanning set. There is a pivot in each column. Every solution is unique. The corresponding system is always solvable. The columns are independent. There is a pivot in each row.

For what value of k will the system have no solutions?

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 = ↓ ↑ ↓ ↑ →

Convert the system Augmented matrix: Echelon form: Is the system consistent? Solution: (21₁, #2) = ( $1 -4x1 -5x1 X1 select V + 13x2 + 16x2 3x2 to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions. + - || - || = 7 8 −1 $1, +