Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Chapter B, Problem 12E
To determine
To fill: The blank to complete the provided statement “
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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
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2) Given the following matrices A =
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1] an
and B =
0
1
-3
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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.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
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Chapter B Solutions
Prealgebra (6th Edition)
Ch. B - Fill in the blanks. 1mi=ftCh. B - Fill in the blanks. 1ft=in.Ch. B - Prob. 3ECh. B - Fill in the blanks. 1qt=galCh. B - Prob. 5ECh. B - Prob. 6ECh. B - Fill in the blanks. 60sec=minCh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Fill in the blanks. 2gal=qtCh. B - Prob. 12ECh. B - Prob. 13ECh. B - Fill in the blanks. 9ft=ydCh. B - Fill in the blanks. 2mi=ftCh. B - Prob. 16ECh. B - Fill in the blanks. 120sec=minCh. B - Prob. 18ECh. B - Prob. 19ECh. B - Fill in the blanks. 4pt=qtCh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Perform the operation indicated. 5ft4in.+4ft3in.Ch. B - Prob. 26ECh. B - Perform the operation indicated. 12ft7in.+3ft8in.Ch. B - Prob. 28ECh. B - Perform the operation indicated. 26yd1ft9yd2ftCh. B - Perform the operation indicated. 14yd6ft6yd2ftCh. B - While golfing, Todd made birdie putts of 4 ft 3...Ch. B - Jessica worked out at the health spa for 2 hr 20...Ch. B - Natalie bought a 1-pint can of tomato sauce. She...Ch. B - Joel has 1 quart of milk. If he uses 1 pint to...Ch. B - It takes Isaac 2 hours to detail a car. Sean can...Ch. B - A 3-pound can of Joes Chili costs the same price...Ch. B - Write the abbreviation for each metric unit....Ch. B - Prob. 38ECh. B - Write the abbreviation for each metric unit....Ch. B - Prob. 40ECh. B - Write the abbreviation for each metric unit....Ch. B - Prob. 42ECh. B - Prob. 43ECh. B - Place the appropriate symbol, or, in the blanks....Ch. B - Prob. 45ECh. B - Place the appropriate symbol, or, in the blanks....Ch. B - Prob. 47ECh. B - Place the appropriate symbol, or, in the blanks....Ch. B - Which of the following represents a unit that is...Ch. B - Which of the following represents a unit that is...Ch. B - Which of the following represents a unit that is...Ch. B - Which of the following represents a unit that is...Ch. B - Place the appropriate symbol, or, in the blanks....Ch. B - Place the appropriate symbol, or, in the blanks....Ch. B - Prob. 55ECh. B - Place the appropriate symbol, or, in the blanks....Ch. B - Place the appropriate symbol, or, in the blanks....Ch. B - Prob. 58ECh. B - Fill in the blanks. The _______ is the basic...Ch. B - Prob. 60ECh. B - Prob. 61ECh. B - Fill in the blanks. The gram is the basic metric...Ch. B - Prob. 63ECh. B - Lisa measured the width of a doorway. Choose the...Ch. B - Choose the unit of measure that best completes the...Ch. B - Choose the unit of measure that best completes the...Ch. B - Use the figure to the right for exercises 67 and...Ch. B - Use the figure to the right for exercises 67 and...Ch. B - Use the following information to answer exercises...Ch. B - Use the following information to answer exercises...
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- 10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.arrow_forward7) Use the Venn Diagram below to determine the sets A, B, and U. A = B = U = Blue Orange white Yellow Black Pink Purple green Grey brown Uarrow_forward8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.arrow_forward
- 1) Use the roster method to list the elements of the set consisting of: a) All positive multiples of 3 that are less than 20. b) Nothing (An empty set).arrow_forward2) Let M = {all postive integers), N = {0,1,2,3... 100), 0= {100,200,300,400,500). Determine if the following statements are true or false and explain your reasoning. a) NCM b) 0 C M c) O and N have at least one element in common d) O≤ N e) o≤o 1arrow_forward4) Which of the following universal sets has W = {12,79, 44, 18) as a subset? Choose one. a) T = {12,9,76,333, 44, 99, 1000, 2} b) V = {44,76, 12, 99, 18,900,79,2} c) Y = {76,90, 800, 44, 99, 55, 22} d) x = {79,66,71, 4, 18, 22,99,2}arrow_forward
- 3) What is the universal set that contains all possible integers from 1 to 8 inclusive? Choose one. a) A = {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8} b) B={-1,0,1,2,3,4,5,6,7,8} c) C={1,2,3,4,5,6,7,8} d) D = {0,1,2,3,4,5,6,7,8}arrow_forwardA smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…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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