1. A system of linear equations can be described in a matrix equation Ax = b with [2 -1 1] A = |1 1 2, x L-1 5 4] and b = |b2 a. Determine if the columns of the matrix A span R³. Give your arguments. b. If the system is homogeneous, describe the trivial solution of the system (if any) in parametric vector form. Also, give a geometric description of the solution set. Give the clear argument. c. If the system is nonhomogeneous and consistent, describe b in parametric vector form. Give the clear argument. d. If b, = 5,b2 = -3, b3 = 0, is the system consistent? Give valid argument. Find the solution set of the system. Compare the solution set with the trivial solution of the homogeneous system in b.

Suppose the solution set of a system of linear equations can be described as x₁ = 2-5x4 x₂ = -4x4 x3 = 5 +9x4 with 4 free. a. Write the solution to this system in parametric vector form. x = DNE x+x4

Determine whether the statement below is true or false. Justify the answer. The equation Ax = b is homogeneous if the zero vector is a solution. Choose the correct answer below. OA. The statement is false. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in R™. Thus, the zero vector is never a solution of a homogeneous system. B. The statement is true. A system of linear equations is said to be homogeneous if it can be written in the form Ax=b, where A is an mxn matrix and b is a nonzero vector in R™. If the zero vector is a solution, then b = 0. C. The statement is true. A system of linear equations is said to be homogeneous if it can be written in the form Ax = 0, where A is an mxn matrix and 0 is the zero vector in R™. If the zero vector is a solution, then b = Ax = A0 = 0. O D. The statement is false. A system of linear equations is said to be homogeneous if it can be written in the form…

Use matrix inversion to solve the given system of linear equations. X3 X2 + y 12 = 3 + y = 5 (x, y) = × )

Solve the homogeneous system of equations whose coefficient matrix is 1 -2 -2 2 2 -4 -4 1 1 1 1 A = -2 solutions. 1 2 -1 -4 2 4 8 10 Write the solution set as a linear combination of basic