EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 58, Problem 5AR
Express 64.1420° as degrees, minutes, and seconds.
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5) State any theorems that you use in determining your solution.
a) Suppose you are given a model with two explanatory variables such that:
Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n
Using partial differentiation derive expressions for the intercept and slope
coefficients for the model above.
[25 marks]
b)
A production function is specified as:
Yi = α + B₁x1i + ẞ2x2i + Ui,
i = 1, 2, ... n,
u₁~N(0,σ²)
where:
y = log(output), x₁ = log(labor input), x2 = log(capital input)
The results are as follows:
x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10,
= 8, Syy = 10,
S2y
n = 23 (individual firms)
i) Compute values for the intercept, the slope coefficients and σ².
[20 marks]
ii)
Show that SE (B₁) = 0.102.
[15 marks]
iii)
Test the hypotheses: ẞ1
=
1 and B2 = 0, separately at the 5%
significance level. You may take without calculation that SE (a) = 0.78
and SE (B2) = 0.102
[20 marks]
iv)
Find a 95% confidence interval for the estimate ẞ2.
[20 marks]
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of 2
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The set of all 3 x 3 upper triangular matrices
6) Determine whether each of the following sets, together with the standard
operations, is a vector space. If it is, then simply write 'Vector space'. You do not
have to prove all ten vector space axioms. If it is not, then identify one of the ten
vector space axioms with its number in the attached sheet that fails and also show
that how it fails.
a) The set of all polynomials of degree four or less.
b) The set of all 2 x 2 singular matrices.
c) The set {(x, y) : x ≥ 0, y is a real number}.
d) C[0,1], the set of all continuous functions defined on the interval [0,1].
7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and
show that it is orthogonal to both u and v.
8) a) Find the equation of the least squares regression line for the data points
below.
(-2,0), (0,2), (2,2)
b) Graph the points and the line that you found from a) on the same Cartesian
coordinate plane.
Page <
1
of 2
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ZOOM +
1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
Chapter 58 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 58 - Add, subtract, multiply, or divide each of the...Ch. 58 - Determine A.Ch. 58 - Prob. 3ARCh. 58 - Express 68.85 as degrees and minutes.Ch. 58 - Express 64.1420 as degrees, minutes, and seconds.Ch. 58 - Express 3723' as decimal degrees to 2 decimal...Ch. 58 - Express 10338'43" as decimal degrees to 4 decimal...Ch. 58 - Using a simple protractor, measure each of the...Ch. 58 - Prob. 9ARCh. 58 - Write the complement of each of the following...
Ch. 58 - Write the complement of each of the following...Ch. 58 - Given: ABCD and FEGH . Determine the value of each...Ch. 58 - a. Determine: (1) 1 (2) Side a b. Determine: (1) 1...Ch. 58 - a. Given: a=8.400 and b=9.200 . Find c. b. Given:...Ch. 58 - Compute 1.Ch. 58 - Determine the circumference of a circle that has a...Ch. 58 - Determine the diameter of a circle that has a...Ch. 58 - a. Given: CD=184 mm and CE=118 mm. Determine CF...Ch. 58 - a. Given: EB=5.150. Determine AE . b. Given:...Ch. 58 - Given: Points A and E are tangent points. EB is a...Ch. 58 - a. Given: AC=110andr=4.700 Compute arc length AC...Ch. 58 - a. Given: Dia H=14.520 and d=8.300. Compute Dia M....Ch. 58 - Prob. 23ARCh. 58 - a. Given: x=360 inches and y=5.10 inches. Compute...Ch. 58 - Prob. 25ARCh. 58 - A flat is cut on a circular piece as shown....Ch. 58 - A spur gear is shown. Pitch circles of spur gears...Ch. 58 - Determine the arc length from point C to point D...Ch. 58 - Prob. 29ARCh. 58 - Determine dimension x to 3 decimal places.Ch. 58 - Refer to the drill jig shown. Determine 1.Ch. 58 - Prob. 32ARCh. 58 - Prob. 33ARCh. 58 - Lay out the template shown. Make the layout full...
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- Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is givenarrow_forwardplease help me with this question with working out thanksarrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forward
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