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Matrices & Determinants Questions

Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z.
x-10y-35z=3
-5x+11y+58z=-15
x-2y-11x=3

x=________________
y=________________
z=____

Math

Matrices & Determinants Solutions

Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. x-10y-35z=3 -5x+11y+58z=-15 x-2y-11x=3 x=________________ y=________________ z=________________

For the game, if a saddle point exists, find the strategies producing it and the value of the game. Identify whether the game is strictly determined
[-2 1]
[9 4]
Select the correct choice below and, if necessary, fill in the a

Math

Matrices & Determinants Solutions

For the game, if a saddle point exists, find the strategies producing it and the value of the game. Identify whether the game is strictly determined [-2 1] [9 4] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A). The saddle point(s) is/are produced by the strategies described by the ordered pair(s)____ The value of the game is_____ B). There is no saddle point

In the following game, decide on the payoff when the strategy (3,1) is used. Assume that the payoff amounts given are in dollars.
1 2 3
1 [12 -11 0]
2 [7 -10 8]

Math

Matrices & Determinants Solutions

In the following game, decide on the payoff when the strategy (3,1) is used. Assume that the payoff amounts given are in dollars. 1 2 3 1 [12 -11 0] 2 [7 -10 8] 3[- 6 3 11] When the strategy (3,1) is used, the payoff is $

Math

Matrices & Determinants Solutions

How many solutions does the following system have?
2x + y + z=2
2x - 2y - 3z=2
10x - 3y - 4z=-1

Select the correct answer below:
a) No solutions
b)l solution
c)Infinitely many solutions

Math

Matrices & Determinants Solutions

How many solutions does the following system have? 2x + y + z=2 2x - 2y - 3z=2 10x - 3y - 4z=-1 Select the correct answer below: a) No solutions b)l solution c)Infinitely many solutions

Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W.
y = 4 u₁ = 1 u₂ = -1 u₃ = -1
2 1 3 0
2 0

Math

Matrices & Determinants Solutions

Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. y = 4 u₁ = 1 u₂ = -1 u₃ = -1 2 1 3 0 2 0 1 1 -1 1 -2 1

$Solve the system by using Gaussian elimination or Gauss-Jordan elimination. -5x -9y +10z = 30 x +2y +2z = 2 -4x - 2y –9z = - -10 The solution set is { __ , __ , __ }$

Math

Matrices & Determinants Solutions

Solve the system by using Gaussian elimination or Gauss-Jordan elimination. -5x -9y +10z = 30 x +2y +2z = 2 -4x - 2y –9z = - -10 The solution set is { __ , __ , __ }

A certain experiment produces the data (1, 1.7), (2, 2.6), (3, 3.2), (4, 3.6), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y = β1*x+ β2*x^2. Such a function might arise, for example, as

Math

Matrices & Determinants Solutions

A certain experiment produces the data (1, 1.7), (2, 2.6), (3, 3.2), (4, 3.6), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y = β1*x+ β2*x^2. Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price to be set for the product. Answer parts (a) through (c) below. a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. The observation vector is y = Choose the correct form of the parameter vector β below. b. Find the associated least-squares curve for the data. c. If a machine learned the curve you found in (b), what output would it provide for an input of x = 6?

Let the matrix below be the augmented matrix [A|B] of a linear system Ax = b. Write the most general solution (the sum of a particular one and the general solution of the homogeneous system) in parametric form. Write it in vector form. Give a basis o

Math

Matrices & Determinants Solutions

Let the matrix below be the augmented matrix [A|B] of a linear system Ax = b. Write the most general solution (the sum of a particular one and the general solution of the homogeneous system) in parametric form. Write it in vector form. Give a basis of NulA. 0 2 0 0 2 0 0 1 0 3 0 0 0 1 2

Use the inverse of the coefficient matrix to solve the system of equations.
x + 4y + 3z = - 26
x - 3y - 2z = 11
2x + 5y + 4z = -11
(x,y,z)= (__,__,__)

Math

Matrices & Determinants Solutions

Use the inverse of the coefficient matrix to solve the system of equations. x + 4y + 3z = - 26 x - 3y - 2z = 11 2x + 5y + 4z = -11 (x,y,z)= (__,__,__)

$(a) Show that the vectors v1 = (1,2,1,0), v2 = (2,6,0,2) and v3 = (3,7,2,2) form a linearly independent set in R^4. (b) Find a fourth vector v4 in R^4 such that {V1, V2, V3, V4} is a linearly independent set in R^4. (c) Explain, stating and using a r$

Math

Matrices & Determinants Solutions

(a) Show that the vectors v1 = (1,2,1,0), v2 = (2,6,0,2) and v3 = (3,7,2,2) form a linearly independent set in R^4. (b) Find a fourth vector v4 in R^4 such that {V1, V2, V3, V4} is a linearly independent set in R^4. (c) Explain, stating and using a result from Section 5 in the Course Notes, why your set {v1, v2, v3, v4} is a basis of R4. (d) What is the row rank of the matrix: A= 1 2 1 0 2 6 0 2 3 7 2 2

Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Sean stayed in three different cities (Washington, D.C., Atlanta, Georgia, and Dallas, Texas) for a total of 11

Math

Matrices & Determinants Solutions

Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Sean stayed in three different cities (Washington, D.C., Atlanta, Georgia, and Dallas, Texas) for a total of 11 nights. He spent twice as many nights in Dallas as he did in Washington. The total cost for 11 nights (excluding tax) was $1830. Determine the number of nights that he spent in each city. City Cost per Night Washington $230 Cost per Night $ 120 Dallas $ 150 sean spent____ night(s) in washington.______night(s) in Atlanta, and ___night(s) in dallas

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