Mathematics: A Discrete Introduction
3rd Edition
ISBN: 9780840049421
Author: Edward A. Scheinerman
Publisher: Cengage Learning
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Textbook Question
Chapter 1.5, Problem 5.12E
Suppose a, b, c, and d are integers. Prove that if
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The 2x2 linear system of equations -2x+4y = 8 and 4x-3y = 9 was put into the following
-2 4
8
augmented matrix:
4
-3
9
This augmented matrix is then converted to row echelon form. Which of the following matrices is the
appropriate row echelon form for the given augmented matrix?
0
Option 1:
1
11
-2
Option 2:
4
-3 9
Option 3:
10
܂
-2
-4
5
25
1
-2
-4
Option 4:
0 1
5
1 -2
Option 5:
0
0
20
-4
5
○ Option 1 is the appropriate row echelon form.
○ Option 2 is the appropriate row echelon form.
○ Option 3 is the appropriate row echelon form.
○ Option 4 is the appropriate row echelon form.
○ Option 5 is the appropriate row echelon form.
Let matrix A have order (dimension) 2x4 and let matrix B have order (dimension) 4x4.
What results when you compute A+B?
The resulting matrix will have dimensions of 2x4.
○ The resulting matrix will be a single number (scalar).
The resulting matrix will have dimensions of 4x4.
A+B is undefined since matrix A and B do not have the same dimensions.
If
-1
"[a446]-[254]
4b
=
-1
, find the values of a and b.
○ There is no solution for a and b.
○ There are infinite solutions for a and b.
O a=3, b=3
O a=1, b=2
O a=2, b=1
O a=2, b=2
Chapter 1 Solutions
Mathematics: A Discrete Introduction
Ch. 1.1 - Simplify the following algebraic expression:...Ch. 1.2 - Prob. 2.1ECh. 1.3 - Prob. 3.1ECh. 1.3 - Prob. 3.2ECh. 1.3 - Prob. 3.3ECh. 1.3 - Prob. 3.4ECh. 1.3 - Prob. 3.5ECh. 1.3 - Prob. 3.6ECh. 1.3 - Prob. 3.7ECh. 1.3 - Prob. 3.8E
Ch. 1.3 - Prob. 3.9ECh. 1.3 - Prob. 3.10ECh. 1.3 - Prob. 3.11ECh. 1.3 - Prob. 3.12ECh. 1.3 - Prob. 3.13ECh. 1.3 - Prob. 3.14ECh. 1.4 - Prob. 4.1ECh. 1.4 - Prob. 4.2ECh. 1.4 - Prob. 4.3ECh. 1.4 - Prob. 4.4ECh. 1.4 - Prob. 4.5ECh. 1.4 - Prob. 4.6ECh. 1.4 - Prob. 4.7ECh. 1.4 - Prob. 4.8ECh. 1.4 - Prob. 4.9ECh. 1.4 - Prob. 4.10ECh. 1.4 - Prob. 4.11ECh. 1.4 - Prob. 4.12ECh. 1.5 - Prove that the sum of two odd integers is even.Ch. 1.5 - Prove that the sum of an odd integer and an even...Ch. 1.5 - Prove that if n is an odd integer, then n is also...Ch. 1.5 - Prove that the product of two even integers is...Ch. 1.5 - Prove that the product of an even integer and an...Ch. 1.5 - Prove that the product of two odd integers is odd.Ch. 1.5 - Prove that the square of an odd integer is odd.Ch. 1.5 - Prove that the cube of an odd integer is odd.Ch. 1.5 - Suppose a, b, and c are integers. Prove that if ab...Ch. 1.5 - Suppose a, b, and c are integers. Prove that if...Ch. 1.5 - Suppose a, b, d, x, and y are integers. Prove that...Ch. 1.5 - Suppose a, b, c, and d are integers. Prove that if...Ch. 1.5 - Let x be an integer. Prove that x is odd if and...Ch. 1.5 - Let x be an integers. Prove that x is odd if and...Ch. 1.5 - Let x be an integer. Prove that 0x if and only if...Ch. 1.5 - Let a and b be integers. Prove that ab if and only...Ch. 1.5 - Let a be a number with a1. Prove that a number x...Ch. 1.5 - Prove that the difference between consecutive...Ch. 1.5 - Let a be a perfect square. Prove that a is the...Ch. 1.5 - For real numbers a and b, prove that if 0ab, then...Ch. 1.5 - Prove that the difference between distinct,...Ch. 1.5 - Prove that an integer is odd if and only if it is...Ch. 1.5 - Suppose you are asked to prove a statement of the...Ch. 1.5 - Suppose you are asked to prove a statement of the...Ch. 1.6 - Disprove: If a and b are integers with ab, then...Ch. 1.6 - Disprove: If a and b are nonnegative integers with...Ch. 1.6 - Disprove: If a, b, and c are positive integers...Ch. 1.6 - Disprove: If a, b, and c are positive integers,...Ch. 1.6 - Disprove: If p and q are prime, then p+q is...Ch. 1.6 - Disprove: If p is prime, then 2p1 is also prime.Ch. 1.6 - Prob. 6.7ECh. 1.6 - An integer is a palindrome if it reads the same...Ch. 1.6 - Prob. 6.9ECh. 1.6 - Prob. 6.10ECh. 1.6 - Prob. 6.11ECh. 1.6 - Prob. 6.12ECh. 1.6 - Prob. 6.13ECh. 1.7 - Prob. 7.1ECh. 1.7 - Prob. 7.2ECh. 1.7 - Prob. 7.3ECh. 1.7 - Prob. 7.4ECh. 1.7 - Prob. 7.5ECh. 1.7 - Prob. 7.6ECh. 1.7 - Prob. 7.7ECh. 1.7 - Prob. 7.8ECh. 1.7 - Prob. 7.9ECh. 1.7 - Prob. 7.10ECh. 1.7 - Prob. 7.11ECh. 1.7 - Prob. 7.12ECh. 1.7 - Prob. 7.13ECh. 1.7 - Prob. 7.14ECh. 1.7 - Prob. 7.15ECh. 1.7 - Prob. 7.16ECh. 1.7 - Prob. 7.17ECh. 1.7 - Prob. 7.18ECh. 1.7 - Prove that xy can be reexpressed in terms of just ...Ch. 1.7 - Prob. 7.20ECh. 1 - Prob. 1STCh. 1 - Prob. 2STCh. 1 - Prob. 3STCh. 1 - Prob. 4STCh. 1 - Prob. 5STCh. 1 - Prob. 6STCh. 1 - Prob. 7STCh. 1 - Prob. 8STCh. 1 - Prob. 9STCh. 1 - Prob. 10STCh. 1 - Prob. 11STCh. 1 - Prob. 12STCh. 1 - Prob. 13STCh. 1 - Prob. 14STCh. 1 - Prob. 15STCh. 1 - Prob. 16STCh. 1 - Prob. 17STCh. 1 - Prob. 18STCh. 1 - Prob. 19STCh. 1 - Prob. 20ST
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