Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 3, Problem 2A
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5. The volume V of a given mass of
monoatomic gas changes with temperat re
T according to the relation
V = KT2/3. The work done when
temperature changes by 90 K will be xR.
The value of x is
(a) 60
(b)20
(c)30
S
(d)90
Consider a matrix
3
-2
1
A =
0
5 4
-6
2
-1
Define matrix B as transpose of the inverse of matrix A. Find the determinant of matrix A + B.
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]
Chapter 3 Solutions
Mathematics For Machine Technology
Ch. 3 - Determine the least common denominator of 23,58,...Ch. 3 - Express 14,56, and 712as equivalent fractions...Ch. 3 - Express 298 as a mixed number.Ch. 3 - Express the mixed number 516as an improper...Ch. 3 - Add 512+34+16 .Ch. 3 - Add 238+134+513 .Ch. 3 - Subtract each of the fractions in Exercises 7...Ch. 3 - Subtract each of the fractions in Exercises 7...Ch. 3 - Subtract each of the fractions in Exercises 7...Ch. 3 - Prob. 10A
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- please 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_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).arrow_forward
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