solve question (d)(e) with explanation asap
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- Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns whose solution space consists of those vectors in R^3 tha are orthogonal to a=(-3,2,-1) and b=(0,-2,-2)From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.
- Let x be a solution to the m × n homogeneous linear system of equations Ax = 0. Explain why x is orthogonal to the row vectors of A.A three particle system with with masses: m1 = 5.0 Kg, m2 = 3.0 Kg and m3 = 5.0 Kg. The position co-ordinates for particle 1 are (4,4), for particle 2 are (2,1) and for particle 3 are (1,2). What will be the x coordinate of the system s center of mass?If A is invertible, i.e., for any given r.h.s. vector b, the system Ax = b has a solution. How can you compute the 3rd column of A^−1(what r.h.s. b would youchoose)?
- 1.Find the x- and y-Nullclines of the system and sketch them.How many equilibria are there? Where are they located? 2.The Nullclines separate the plane into regions where solutionsare generally moving in the same direction. For each region in your plot,indicate the general direction that solutions are moving (e.g. “Northeast”or “Down-and-right”). 3. A region is called “positively invariant” if solutions in thatregion stay in that region as time increases. Which regions of your plot arepositively invariant? 4. Use your answers to the previous parts (NOT the linearizationtheorem) to classify each equilibria as a source, a sink, a saddle, or noneof the above. 5. describe the long-term behavior of everysolution in the plane. You should explain what can happen as t → ∞ andqualitatively describe which solutions have each behavior.Solve the system ax - by - 2cz = 21, ax + by + cz = 0 and 2ax - by + cz = 14 for (x, y, z) in terms of the nonzero constants a, b, and c.Find general solutions of the systems in Problem Attached.