Suppose the solution set of a certain system of linear equations can be described as ×₁ = 6+5x3, x2 = -3-9x3, with X3 free. Use vectors to describe this set as a line in R³. Geometrically, the solution set is a line through parallel to

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

A hiker is returning to a campsite that is 5 miles east and 2 miles south fromtheir current position. The hiker is currently walking east along a path at a pace of 4 milesper hour. The hiker plans to leave the path and walk in a straight line diagonally towardsthe cabin through the woods. The hiker can only walk at a pace of 3 miles per hour throughthe woods. Where should the hiker leave the path and turn into the woods if they want toget to the campsite as quickly as possible?

Consider the following system of linear equations: -11x + 3y +-31z = 118 -4x + 1y+-11z = 42