A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Chapter 5.2B, Problem 23A
To determine
a)
To find:
The integer value of
To determine
b)
To find:
The integer value of
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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.
Find the Laplace Transform of the function to express it in frequency domain form.
Please draw a graph that represents the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
Chapter 5 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Ch. 5.1 - A turnpike driver had car trouble. He knew that he...Ch. 5.1 - Prob. 2MCCh. 5.1 - Prob. 3MCCh. 5.1 - Prob. 4MCCh. 5.1 - Prob. 5MCCh. 5.1 - Prob. 6MCCh. 5.1 - Describe a realistic word problem that models...Ch. 5.1 - Prob. 8MCCh. 5.1 - Prob. 9MCCh. 5.1 - Investigate how tides are measured and design an...
Ch. 5.1 - A fourth-grade student devised the following...Ch. 5.1 - Prob. 14MCCh. 5.1 - MATHEMATICAL CONNECTIONS A student had the...Ch. 5.1 - Prob. 16MCCh. 5.1 - Prob. 17MCCh. 5.1 - Prob. 1NAEPCh. 5.1 - Prob. 2NAEPCh. 5.1A - Find the additive inverse of each of the following...Ch. 5.1A - Simplify each of the following expressions. a. (2)...Ch. 5.1A - Evaluate each of the following expressions. a. |5|...Ch. 5.1A - Demonstrate each of the following additions using...Ch. 5.1A - Demonstrate each of the additions in Exercise 4...Ch. 5.1A - Use the absolute value definition of addition to...Ch. 5.1A - Prob. 7ACh. 5.1A - Prob. 8ACh. 5.1A - Prob. 9ACh. 5.1A - Prob. 10ACh. 5.1A - Prob. 11ACh. 5.1A - Prob. 12ACh. 5.1A - Prob. 13ACh. 5.1A - Compute each of following expression. a. 2+(310)...Ch. 5.1A - Prob. 15ACh. 5.1A - Simplify each of the following expressions as much...Ch. 5.1A - For which integers a, b and c does ab+c=a(bc)?...Ch. 5.1A - Prob. 18ACh. 5.1A - Place the integers 4,3,2,0,1,2,3,4 in the grid to...Ch. 5.1A - Let y=x1. Find the value of y in parts a-d when x...Ch. 5.1A - Determine the number of terms in the arithmetic...Ch. 5.1A - Prob. 22ACh. 5.1A - Find the sum of the terms in the following...Ch. 5.1A - How could you explain the time change from the...Ch. 5.1A - Prob. 25ACh. 5.1A - Prob. 26ACh. 5.1A - Find all integer x, if there are any, such that...Ch. 5.1A - In each of the following equations, find all...Ch. 5.1A - An arithmetic sequence may have a positive or...Ch. 5.1A - Prob. 30ACh. 5.1A - Solve the following equations. a. x+7=3 b. 10+x=7...Ch. 5.1A - Prob. 32ACh. 5.1B - ASSESSMENT Find the additive inverse of each of...Ch. 5.1B - ASSESSMENT Simplify each of the following...Ch. 5.1B - ASSESSMENT Evaluate each of the following...Ch. 5.1B - Prob. 5ACh. 5.1B - Prob. 6ACh. 5.1B - Prob. 7ACh. 5.1B - Prob. 8ACh. 5.1B - Prob. 9ACh. 5.1B - Prob. 10ACh. 5.1B - Prob. 11ACh. 5.1B - Prob. 12ACh. 5.1B - Prob. 13ACh. 5.1B - ASSESSMENT Compute each of the following. a....Ch. 5.1B - Prob. 15ACh. 5.1B - ASSESSMENT Simplify each of the following...Ch. 5.1B - Prob. 17ACh. 5.1B - Prob. 18ACh. 5.1B - Prob. 19ACh. 5.1B - ASSESSMENT Let y=3x2. Find the value of y in parts...Ch. 5.1B - Prob. 21ACh. 5.1B - Prob. 22ACh. 5.1B - Prob. 23ACh. 5.1B - Prob. 24ACh. 5.1B - Prob. 25ACh. 5.1B - ASSESSMENT Find all integers x, if there are any,...Ch. 5.1B - ASSESSMENT Let y=|x5|. Find the value of y in...Ch. 5.1B - Prob. 28ACh. 5.1B - ASSESSMENT An arithmetic sequence may have a...Ch. 5.1B - Prob. 30ACh. 5.1B - Prob. 31ACh. 5.1B - Prob. 32ACh. 5.2 - Explain whether (xy)(x+y) can be multiplied by...Ch. 5.2 - We use the equation (a+b)2=a2+2ab+b2 to find a...Ch. 5.2 - Consider the argument to show that (a)(b)=(ab) for...Ch. 5.2 - Prob. 4MCCh. 5.2 - Explain how to find the number of integers between...Ch. 5.2 - Prob. 6MCCh. 5.2 - Prob. 7MCCh. 5.2 - Prob. 8MCCh. 5.2 - Prob. 9MCCh. 5.2 - Prob. 10MCCh. 5.2 - Prob. 11MCCh. 5.2 - A seventh-grade student does not believe 52.The...Ch. 5.2 - A student computes 82(3) by writing 10(3)=30. How...Ch. 5.2 - Prob. 16MCCh. 5.2 - Mariyana felt that using absolute values with...Ch. 5.2 - Prob. 18MCCh. 5.2 - Prob. 19MCCh. 5.2 - Prob. 20MCCh. 5.2 - Prob. 21MCCh. 5.2 - Prob. 22MCCh. 5.2 - Prob. 1NAEPCh. 5.2 - Prob. 2NAEPCh. 5.2A - Use patterns to show that (1)(1)=1Ch. 5.2A - Prob. 2ACh. 5.2A - Prob. 3ACh. 5.2A - Prob. 4ACh. 5.2A - The number of students eating in the school...Ch. 5.2A - Use the definition of division to find each...Ch. 5.2A - Evaluate each of the following expressions, if...Ch. 5.2A - Evaluate each of the following products and then,...Ch. 5.2A - In each of the following, x and y are integers;y0....Ch. 5.2A - In a lab, the temperature of various chemical...Ch. 5.2A - The farmland acreage lost to family dwellings over...Ch. 5.2A - Illustrate the distributive property of...Ch. 5.2A - Compute each of the following. a. (2)3 b. (2)4 c....Ch. 5.2A - If x is an integer and x0, which of the following...Ch. 5.2A - Find all integer values of x for which the...Ch. 5.2A - Prob. 16ACh. 5.2A - Identify the property of integers being...Ch. 5.2A - Prob. 18ACh. 5.2A - Multiply each of the following and combine terms...Ch. 5.2A - Find all integers x if any each of the following....Ch. 5.2A - Use the difference-of-squares formula to simplify...Ch. 5.2A - Factor each of the following expressions...Ch. 5.2A - Prob. 23ACh. 5.2A - Prob. 24ACh. 5.2A - Find the missing terms in the following arithmetic...Ch. 5.2A - A hot air balloon descends at the rate of...Ch. 5.2A - Prob. 27ACh. 5.2B - Use patterns to show that (2)(2)=4.Ch. 5.2B - Prob. 2ACh. 5.2B - Prob. 3ACh. 5.2B - In each of the following charged-field models, the...Ch. 5.2B - Prob. 5ACh. 5.2B - Prob. 6ACh. 5.2B - Prob. 7ACh. 5.2B - Prob. 8ACh. 5.2B - Prob. 9ACh. 5.2B - Prob. 10ACh. 5.2B - Prob. 11ACh. 5.2B - Prob. 12ACh. 5.2B - Compute each of the following. a. 10312 b. 10(312)...Ch. 5.2B - Prob. 14ACh. 5.2B - Identify the property of integers being...Ch. 5.2B - Prob. 16ACh. 5.2B - Multiply each of the following and combine terms...Ch. 5.2B - Find all integers x if any that make the...Ch. 5.2B - Use the difference of squares formula to simplify...Ch. 5.2B - Factor each of the following expressions...Ch. 5.2B - Prob. 21ACh. 5.2B - In each of the following, find the next two terms....Ch. 5.2B - Prob. 23ACh. 5.2B - Prob. 24ACh. 5.2B - Prob. 25ACh. 5.2B - Prob. 26ACh. 5.2B - Prob. 27ACh. 5.CR - Find the additive inverse of each of the...Ch. 5.CR - Prob. 2CRCh. 5.CR - For each of the following, find all possible...Ch. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Simplify each of the following expressions. a. 1x...Ch. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - In each part of exercise 11, if a sequence is...Ch. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Prob. 18CRCh. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CRCh. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CR - The drawing below depicts an elevator. Explain...Ch. 5.CR - Prob. 25CRCh. 5.CR - Prob. 26CRCh. 5.CR - Prob. 27CRCh. 5.CR - Prob. 28CRCh. 5.CR - Prob. 29CRCh. 5.CR - Prob. 30CRCh. 5 - Now Try this 1 Explain whether the sum of two...Ch. 5 - Prob. 2NTCh. 5 - Now Try this 2 Model the subtraction 43 on a...Ch. 5 - Prob. 4NT
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