Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 30, Problem 1A
To determine
To find, the maximum and minimum diameters of the shaft.
Expert Solution & Answer
Answer to Problem 1A
Maximum shaft diameter
Minimum shaft diameter
Explanation of Solution
Given information:
A shaft has a diameter of
Calculation:
Basic shaft diameter is
Tolerance is
Now,
The maximum diameter of the shaft is
The minimum diameter of the shaft is
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LARLINALG8 6.4.013.
Let B = {(1, 3), (-2, -2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let
42
- [13]
A =
30
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from B' to B.
6
4
P =
9
4
(b) Use the matrices P and A to find [v] B and [T(V)] B, where
[v]B[31].
26
[V] B =
->
65
234
[T(V)]B=
->
274
(c) Find P-1 and A' (the matrix for T relative to B').
-1/3
1/3
-
p-1 =
->
3/4
-1/2
↓ ↑
-1
-1.3
A' =
12
8
↓ ↑
(d) Find [T(v)] B' two ways.
4.33
[T(v)]BP-1[T(v)]B =
52
4.33
[T(v)]B' A'[V]B' =
52
目
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DETAILS
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LARLINALG8 7.2.001.
1. [-/2.85 Points]
Consider the following.
-14 60
A =
[
-4-5
P =
-3 13
-1 -1
(a) Verify that A is diagonalizable by computing P-1AP.
P-1AP =
具首
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
(11, 12) =
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LARLINALG8 7.2.007.
For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.)
P =
A =
12 -3
-4
1
Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal.
P-1AP =
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3. [-/2.85 Points]
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LARLINALG8 7.1.021.
Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix.
2 -2 5
0 3 -2
0-1 2
(a) the characteristic equation
(b) the eigenvalues (Enter your answers from smallest to largest.)
(1, 2, 13) =
·( )
a basis for each of the corresponding eigenspaces
X1
x2
=
x3 =
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LARLINALG8 7.1.041.
Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated list.)
λ=
1 0 1
045
002
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Chapter 30 Solutions
Mathematics For Machine Technology
Ch. 30 - Prob. 1ACh. 30 - Prob. 2ACh. 30 - Prob. 3ACh. 30 - Prob. 4ACh. 30 - Prob. 5ACh. 30 - Prob. 6ACh. 30 - Fractional-Inch Steel Rules Read measurements on...Ch. 30 - Prob. 8ACh. 30 - Read measurements on the enlarged fractional rule...Ch. 30 - Read measurements w-z on the enlarged fractional...
Ch. 30 - Prob. 11ACh. 30 - Prob. 12ACh. 30 - Prob. 13ACh. 30 - Prob. 14ACh. 30 - Prob. 15ACh. 30 - Prob. 16ACh. 30 - Decimal-Inch Steel Rules Read measurements a-d on...Ch. 30 - Prob. 18ACh. 30 - Prob. 19ACh. 30 - Prob. 20ACh. 30 - In Exercises 21 and 22, measure the length of each...Ch. 30 - Prob. 22ACh. 30 - Prob. 23ACh. 30 - Prob. 24ACh. 30 - Prob. 25ACh. 30 - Prob. 26ACh. 30 - Read measurements w-zon the enlarged fractional...Ch. 30 - Prob. 28ACh. 30 - Prob. 29ACh. 30 - Measure the lengths of dimensions a-f in Figure...Ch. 30 - Measure the lengths of g-k in Figure 30-26 to the...
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