How many solutions will the linear system Ax = b have if b is in the column space of A and the column vectors of A are linearly dependent? Explain.

6. Consider the following system of four linear equations in five variables. 2x1 + 4x2 – 2x3 + 2x4 + 4x3 = 2 xị+ 2x2 – x3+ 2x4 = 4 3x1 + 6x2 – 2x3 + x4 + 9x5 = 1 5x1 + 10r2 – 4x3 + 5x4 + 9x5 = 9 | (a) Write a vector equation that is equivalent to this linear system, and a matrix equation that is equivalent to this linear system. (b) Determine the solution set of this linear system, and express it in parametric vector form.

Answer only part c

Describe the solution set, x= x₂, of x₁ + 4x2 - 7x3 = -6 in parametric vector form. Select the correct choice X3 below and fill in the answer boxes within your choice. (Type an integer or fraction for each matrix element.) O A. X= OB. X= +X3 O C. x= +x₂ O D. X=X₂ +X3 +X3