### Matrices, Eigenvectors, Eigenvalues and Inverses

Please see the attached file for the fully formatted problems.

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Please see the attached file for the fully formatted problems.

Prove that every regular tournament is strong. Hints Here we need to first figure out something more about outdegrees and indegrees and orders of regular digraphs. Try to find a regular digraps with 3, 4, 5 ,6 vertices, and generalize. D is a regular tournament if there is k such that outdegree x = k and indegree x = n-k

I'm attaching a PDF file with a question about finding nonzero subspace along with the property of direct sum. I wonder if anyone who is familiar with Advanced Linear Algebra material and can provide a detail explanation.

Draw the line whose y-intercept is -7 and whose x-intercept is 4.

1. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) 2x - y = 3 2y = 4x - 6 2. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) y = 3(x - 4) 3x - y = 12 3. (Solve sy

Prove that a cyclic group of prime order p has no non-trivial subgroups.

Let G be a finite group of order 2k, k odd, that contains a cyclic group of oder k. Determine a formula to compute the number of subgroups of G that are of odd order.

Prove that Euler's series converges. See attached file for full problem description.

56. If you earned an average of $25,000 over your working life and you retire after 2005 at age 62, 63, or 64, then your annual Social Security benefit will be $7,000, $7500, or $8000 respectively (www.ssa.gov). There is a linear equation that gives the annual benefit b in terms of age a for these three years. Find the equation.

1) What conditions need to be satisfied for a solution of a system of linear inequalities to have it's solution in the first quadrant? Create an example of such a system. 2) Can you give a real world example when the solution of a system of inequalities must be in the first quadrant? 3) Suppose, wheat and sugar are two b

How do you go mathamatically from eq. 12.4 to eq. 12.5 when solving three equations with three unknowns given the summation rules on page 460? Please show all steps of the mathamatical work by hand without using any computer programs

Let n be the set of natural numbers let i and j be seg n Show that det(t sub i, subj (In)) = -1 Where t sub i, subj means transpose any two rows in the identity matrix (In)

1.- A tree is central if its center is K1 and bicentral if its center is K2. Show that every tree is central or bicentral. ( Kn is call complete graph and it if every two of its vertices are adjacent and every vertex has degree n) 2.- Prove taht a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of d

For an integer n, define the graph Tn as follows: Vertices are 2-element subsets of {1,2,...,n}. Two vertices are adjacent if they have one element in common. (a) What are the order and the size of this graph? (b) How many neighbors does each vertex have? (c) Draw T5.

Prove 2?n ≤ n!

1 3 11. Consider (A) = 2 1 (a) Find the eigenvalue and corresponding eigenvectors of A. (b) Determine matrices B and C such that B A C is diagonal. (c) Show the eigenvectors of (A) are linearly independent. (d) Repre

Solve each system by the substitution method. Indicate whether each system is INDEPENDENT, INCONSISTENT or DEPENDENT 1. x+3(y-1)= 11 2(x-y)+8y+28 2. 1/3x-1/6y+1/3 1/6x+1/4y=0 Solve each compound inequity. State the solution set using interval notation and graph it. 3. x <=0 and x+6>3 and 1/4x>3 4. 1/3x>

2. Find the sum: 2+4 +6+...+2n. (Hint: you can use induction) 3. Arc the following statements logically equivalent? (a) ~(p٨q) and (~pV~q) (b) ~(pVq) and (~p٨~q) (e) (A U B)c and Ac ∩ Bc (remember: Ac denotes the complement of the set A)

Complete each problem show work and ad graphs as needed John spent 1/3 of his inheritance on loose women, 1/5 on expensive cigars, and 3/10 on liquor. He invested the rest in lottery tickets. What percent of his inheritance went to lottery tickets? Evaluate the expression: -(2 - 3)4 Fred and Ethel are florists. They a

1. INDEPENDENT LINEAR SYSTEM a. a system with exactly one solution b. an equation that is satisfied by every real number c. equations that are identical d. a system of lines 2. DEPENDENT SYSTEM a. a system that is independent b. a system that depends on a variable c. a system that has no soluti

Write the sets below using interval notation. If the set is empty, write 0 . (a) {y|y> or equal to -2 and y > or equal to 1 } (b) CUD, where C = {y|y>0} D = {y|y>3} where and

Please show all steps and workings clearly and explain in detail how you derive the answers. 1) This question concerns the linear transformation represented by a 3x3 matrix of real numbers. With respect to the standard basis in both the domain and codomain. (a) Determine t

For each system of linear equations.classify the system as "consistent dependent," "consistent independent," or "inconsistent," and tell whether this makes it a unique solution, no solution, or infinately many solutions. 1) Line 1: y=-x + 2 Line 2: y=1/2 x + 2 2) Line 1:y=-2x + 2 Line 2: 2x + y=2 3) Line 1: y=

Sketch the graph: z= f(x,y) where f(x,y)= x^2 + xy ; c=0,1,2,3,-1,-2,-3 Please show/describe all steps AND explain why it is a hyperbola. Also, sketch the graph: z=f(x,y) where f(x,y)= x/y ; c= 0,1,2,3,-1,-2,-3 Please show/describe all steps.

1. A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows a 1 OR a 2? I tried this one and came up with 1/6 but the OR part is kicking my tail. Maybe I am just over thinking this one. 2. A technician is designing a new portable CD player that requires ten batteries fo

Write a system of two equations in two unknowns for each problem. Solve each system by method of choice. 4x+3y=1.45 2x+5y=1.25

1. Explain why vectors QR and RQ are not equivalent. 2. Explain when the elimination method for solving a system of equations is preferable to the substitution method. It is extremely important for you to show your work. This helps me immensely, as I am much better working backwards when it comes to math problems and soluti

1. Solve to the homogenous system of linear equations. {2x - 2y + z = 0 both equations are in the same { {-2x + y + z = 0 I got the following: x = ¾c, y = -c, z = 1/2c 2. Find the real solutions to the system of equations using the addition method. x^2 + 8y^2 = 5 x^2 - 4y^2 = 2 Is there a rea

1. Solve by substitution: x + y = 6 2x - 4y = 0 2. Does the shaded region of the graph of the system of equations x < 3, x + 7< 4 include the point (2, 3)? How do you know? 3. Explain what it means for a system of equations to be inconsistent and how you can tell whether a system is inconsistent usin

4x+y=12 (1) x-y=8(2) 4x+y=12 x-y=8 5x/5 = 20/5 X=4 4(4) =y - 12 16+y = 12 Y =4 I think this would be an example of elimination method for solving a system of equations however I am unsure how it would transfer to substitution method thus I am needing assistance. I am needing this to be illustrated if you wi