For this problem, you may use MATLAB unless directed otherwise. For each set of equations below, (a) Using either rank or RREF information only, determine if the system of equations is consistent (that is. whether it has a solution). If it is consistent, determine what kind of solution it has (a unique solution, or infinitely many). (b) If the system has a unique solution, find it using MATLAB’s \ operator. If it has infin-itely many solutions, determine the solution parametrically (this is most easily done by hand). (c) This part and part (d) refer only to systems 3-5. Note that in these systems each equation has 3 parameters, which represents a plane in 3D. Using the provided .m file as an example, draw each plane and show whether the planes intersect at a point. line. or do not intersect at all. If the planes are expected to intersect but the intersection(s) is not visible in the given bounds for x and y, adjust the range to reveal the intersection(s). Submit your .m file and snapshots of the three 3D plots you generate. (d) (For systems 3-5 only) Comment on your observation of existence/uniqueness of the solutions in light of the intersections that you observe in the plots. For instance, the three planes intersecting at a single point implies that the solution is unique (i.e., the point where they intersect is the common solution that satisfies all equations, which is the point that lies on all three planes). Comment similarly on cases of infinitely many solutions and no solutions. System 1
System 2
System 3
System 4
System 5
—xt+3×2+x3=6 act+3×3 = 5 2×2 +4×3 = 10
—3×1+ 2×2 — 9,1’3 = —13
xi +x2 — 3×3 = —2 + x2 +.r3 — = 2 XI -FX2 -X3=0
Sp+ 7q+9,=2 Sp+4q+6r= I 7p+ + 9r = 4 a—b+c=8 2a+c=5
—2x+3y+z-2=0 —5x+6y+2z-3 = —4x+5y+2:-4=0