
Basic College Mathematics (5th Edition)
5th Edition
ISBN: 9780321950970
Author: Elayn Martin-Gay
Publisher: PEARSON
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Question
Chapter B, Problem 6E
a.
To determine
The number of hospital beds required for 16,000 people.
b.
To determine
The number of people if 21 beds are there in one hospital.
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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.
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
Basic College Mathematics (5th Edition)
Ch. B - Suppose you make $16 per hour.
Calculate your...Ch. B - A lab technician needs a solution containing 20...Ch. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - A car travels at a rate of 57 miles per hour.
How...Ch. B - A tortilla-making machine makes 16 tortillas per...Ch. B - During a flood watch in New Orleans, Louisiana, an...Ch. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 1PFECh. B - Prob. 2PFECh. B - Prob. 3PFECh. B - Prob. 4PFECh. B - Prob. 5PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 9PFECh. B - Prob. 10PFECh. B - Prob. 11PFECh. B - Prob. 12PFECh. B - Prob. 13PFECh. B - Prob. 14PFECh. B - Prob. 15PFECh. B - Prob. 16PFECh. B - Prob. 17PFECh. B - Prob. 18PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 22PFECh. B - Prob. 23PFECh. B - Prob. 24PFECh. B - Prob. 25PFECh. B - Prob. 26PFECh. B - Prob. 27PFECh. B - Prob. 28PFECh. B - Prob. 29PFECh. B - Prob. 30PFECh. B - Prob. 31PFECh. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Note: Exercises 1–41 review operations with...Ch. B - Prob. 35PFECh. B - Prob. 36PFECh. B - Prob. 37PFECh. B - Prob. 38PFECh. B - Prob. 39PFECh. B - Prob. 40PFECh. B - Prob. 41PFECh. B - Prob. 42PFECh. B - Prob. 43PFECh. B - Prob. 44PFECh. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Note: Exercises 42–51 may contain signed numbers....Ch. B - Prob. 48PFECh. B - Prob. 49PFECh. B - Prob. 50PFECh. B - Prob. 51PFE
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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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