EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 69, Problem 27A
Find dimension y.
All dimensions are in inches.
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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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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 69 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 69 - Determine the sizes of Aand Bto the nearest...Ch. 69 - Write the cofunction of the complement of the...Ch. 69 - Determine sec 14.8527 rounded to 5 decimal places.Ch. 69 - A steel forging in the shape of a right circular...Ch. 69 - Prob. 5ACh. 69 - The legs of a right triangle are 718 and 912 ....Ch. 69 - Determine the height of gage blocks required to...Ch. 69 - Determine the height of gage blocks required to...Ch. 69 - In Exercises 9 and 10, determine the height of...Ch. 69 - In Exercises 9 and 10, determine the height of...
Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Solve the following exercises. For customary...Ch. 69 - Find center distance y. All dimensions are in...Ch. 69 - Find inside caliper dimension x. All dimensions...Ch. 69 - Find radius r. All dimensions are in millimeters.Ch. 69 - Find arc dimension x. All dimensions are in...Ch. 69 - Find the depth of cut x. All dimensions are in...Ch. 69 - Find x. All dimensions are in inches.Ch. 69 - Find gage dimension y. All dimensions are in...Ch. 69 - Find y. All dimensions are in inches.Ch. 69 - Find gage dimension x. All dimensions are in...Ch. 69 - Find x. All dimensions are in millimeters.Ch. 69 - Find dimension y. All dimensions are in inches.Ch. 69 - Find y. All dimensions are in inches.Ch. 69 - Find dimension x. All dimensions are in...Ch. 69 - Find x. All dimensions are in inchesCh. 69 - Find distance y. All dimensions are in millimetersCh. 69 - Find dimension y. All dimensions are in inchesCh. 69 - The length L of the point drill with included...Ch. 69 - Determine the lengths of A and B. Round the...
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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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