PRECALCULUS CUSTOM W/MYMTHLAB >IC<
13th Edition
ISBN: 9781269417358
Author: Blitzer
Publisher: PEARSON C
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Chapter 8.5, Problem 76PE
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3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load
which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the
other support. Locate the point of maximum bendin moment and calculate the value
of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end;
272 KN m
30.
90
3.11 (B). A beam, 12 m long, is to be simply supported at 2m from each end and to
carry a U.d.l of 30kN/m together with a 30 KN point load at the right-hand end.
For ease of transportation the beam is to be jointed in two places, one joint being
Situated 5 m from the left-hand end. What load (to the nearest KN) must be
applied to the left-hand end to ensure that there is no B.M. at the joint (i.e. the
joint is to be a point of contraflexure)? What will then be the best position on the
beam for the other joint? Determine the position and magnitude of the maximum
B.M. present on the beam. [114 KN, 1.6 m from r.h. reaction; 4.7 m from 1.h. reaction;
43.35 KN m.]
2. Using vector algebraic operations, if
-
Ả = 2ây – mây – C
-
B = mây tây – 2,
C = ây + mây + 20,
D = m x + mây tậ
Z
Find the value(s) of m such that (a) Ả is
perpendicular to B (b) B is parallel to C
Chapter 8 Solutions
PRECALCULUS CUSTOM W/MYMTHLAB >IC<
Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix
...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVCCh. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVCCh. 8.1 - Prob. 4CVCCh. 8.1 - Fill in each blank so that the resulting statement...
Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 1PECh. 8.1 - Prob. 2PECh. 8.1 - Prob. 3PECh. 8.1 - Prob. 4PECh. 8.1 - Prob. 5PECh. 8.1 - Prob. 6PECh. 8.1 - Prob. 7PECh. 8.1 - Prob. 8PECh. 8.1 - Prob. 9PECh. 8.1 - Prob. 10PECh. 8.1 - Prob. 11PECh. 8.1 - Prob. 12PECh. 8.1 - Prob. 13PECh. 8.1 - Prob. 14PECh. 8.1 - Prob. 15PECh. 8.1 - Prob. 16PECh. 8.1 - Prob. 17PECh. 8.1 - Prob. 18PECh. 8.1 - Prob. 19PECh. 8.1 - Prob. 20PECh. 8.1 - Prob. 21PECh. 8.1 - Prob. 22PECh. 8.1 - Prob. 23PECh. 8.1 - Prob. 24PECh. 8.1 - Prob. 25PECh. 8.1 - Prob. 26PECh. 8.1 - Prob. 27PECh. 8.1 - Prob. 28PECh. 8.1 - Prob. 29PECh. 8.1 - Prob. 30PECh. 8.1 - Prob. 31PECh. 8.1 - Prob. 32PECh. 8.1 - Prob. 33PECh. 8.1 - Prob. 34PECh. 8.1 - Prob. 35PECh. 8.1 - In Exercises 21-38, solve each system of equations...Ch. 8.1 - Prob. 37PECh. 8.1 - In Exercises 21-38. solve each system of equations...Ch. 8.1 - Prob. 39PECh. 8.1 - Prob. 40PECh. 8.1 - Prob. 41PECh. 8.1 - Prob. 42PECh. 8.1 - Prob. 43PECh. 8.1 - Prob. 44PECh. 8.1 - Prob. 45PECh. 8.1 - Prob. 46PECh. 8.1 - Prob. 47PECh. 8.1 - Write a system of linear equations in three or...Ch. 8.1 - Prob. 49PECh. 8.1 - Prob. 50PECh. 8.1 - Prob. 51PECh. 8.1 - Prob. 52PECh. 8.1 - Prob. 53PECh. 8.1 - Describe how to use row operations and matrices to...Ch. 8.1 - What is the difference between Gaussian...Ch. 8.1 - Prob. 56PECh. 8.1 - Prob. 57PECh. 8.1 - Prob. 58PECh. 8.1 - Make Sense? In Exercises 59-62, determine whether...Ch. 8.1 - Prob. 60PECh. 8.1 - Prob. 61PECh. 8.1 - Prob. 62PECh. 8.1 - Prob. 63PECh. 8.1 - Prob. 64PECh. 8.1 - Prob. 65PECh. 8.1 - Prob. 66PECh. 8.1 - Prob. 67PECh. 8.1 - Prob. 68PECh. 8.1 - Prob. 69PECh. 8.1 - Prob. 70PECh. 8.1 - Prob. 71PECh. 8.1 - Prob. 72PECh. 8.1 - Prob. 73PECh. 8.1 - Prob. 74PECh. 8.2 - Check Point 1 Use Gaussian elimination to solve...Ch. 8.2 - Check Point 2 Use Gaussian elimination to solve...Ch. 8.2 - Prob. 3CPCh. 8.2 - Check Point 4 Figure 8.5 shows a system of four...Ch. 8.2 - Prob. 1CVCCh. 8.2 - Prob. 2CVCCh. 8.2 - Prob. 3CVCCh. 8.2 - Prob. 4CVCCh. 8.2 - Prob. 5CVCCh. 8.2 - Prob. 1PECh. 8.2 - Prob. 2PECh. 8.2 - Prob. 3PECh. 8.2 - Prob. 4PECh. 8.2 - Prob. 5PECh. 8.2 - Prob. 6PECh. 8.2 - Prob. 7PECh. 8.2 - Prob. 8PECh. 8.2 - Prob. 9PECh. 8.2 - Prob. 10PECh. 8.2 - Prob. 11PECh. 8.2 - In Exercises 1-24, use Gaussian elimination to...Ch. 8.2 - Prob. 13PECh. 8.2 - Prob. 14PECh. 8.2 - Prob. 15PECh. 8.2 - Prob. 16PECh. 8.2 - Prob. 17PECh. 8.2 - Prob. 18PECh. 8.2 - Prob. 19PECh. 8.2 - Prob. 20PECh. 8.2 - Prob. 21PECh. 8.2 - Prob. 22PECh. 8.2 - Prob. 23PECh. 8.2 - Prob. 24PECh. 8.2 - Prob. 25PECh. 8.2 - Prob. 26PECh. 8.2 - Prob. 27PECh. 8.2 - Prob. 28PECh. 8.2 - Prob. 29PECh. 8.2 - Prob. 30PECh. 8.2 - Prob. 31PECh. 8.2 - Prob. 32PECh. 8.2 - 33. The figure shows the intersections of four...Ch. 8.2 - Prob. 34PECh. 8.2 - Prob. 35PECh. 8.2 - Prob. 36PECh. 8.2 - Prob. 37PECh. 8.2 - Describe what happens when Gaussian elimination is...Ch. 8.2 - Prob. 39PECh. 8.2 - Prob. 40PECh. 8.2 - Prob. 41PECh. 8.2 - Prob. 42PECh. 8.2 - Prob. 43PECh. 8.2 - Prob. 44PECh. 8.2 - Prob. 45PECh. 8.2 - Before beginning this exercise, the group needs to...Ch. 8.2 - Prob. 47PECh. 8.2 - Prob. 48PECh. 8.2 - Prob. 49PECh. 8.2 - Prob. 50PECh. 8.2 - Prob. 51PECh. 8.2 - Prob. 52PECh. 8.2 - Prob. 53PECh. 8.3 - Check Point 1 Let
...Ch. 8.3 - Prob. 2CPCh. 8.3 - Prob. 3CPCh. 8.3 - Prob. 4CPCh. 8.3 - Prob. 5CPCh. 8.3 - Prob. 6CPCh. 8.3 - Prob. 7CPCh. 8.3 - Check Point 8 Change the contrast of the letter L...Ch. 8.3 - Prob. 9CPCh. 8.3 - Prob. 1CVCCh. 8.3 - Prob. 2CVCCh. 8.3 - Prob. 3CVCCh. 8.3 - Prob. 4CVCCh. 8.3 - Prob. 5CVCCh. 8.3 - Prob. 6CVCCh. 8.3 - Prob. 7CVCCh. 8.3 - Prob. 8CVCCh. 8.3 - Prob. 9CVCCh. 8.3 - Prob. 10CVCCh. 8.3 - Prob. 1PECh. 8.3 - Prob. 2PECh. 8.3 - Prob. 3PECh. 8.3 - Prob. 4PECh. 8.3 - Prob. 5PECh. 8.3 - Prob. 6PECh. 8.3 - Prob. 7PECh. 8.3 - Prob. 8PECh. 8.3 - Prob. 9PECh. 8.3 - Prob. 10PECh. 8.3 - Prob. 11PECh. 8.3 - Prob. 12PECh. 8.3 - Prob. 13PECh. 8.3 - Prob. 14PECh. 8.3 - Prob. 15PECh. 8.3 - Prob. 16PECh. 8.3 - Prob. 17PECh. 8.3 - Prob. 18PECh. 8.3 - Prob. 19PECh. 8.3 - Prob. 20PECh. 8.3 - Prob. 21PECh. 8.3 - Prob. 22PECh. 8.3 - Prob. 23PECh. 8.3 - Prob. 24PECh. 8.3 - Prob. 25PECh. 8.3 - Prob. 26PECh. 8.3 - Prob. 27PECh. 8.3 - Prob. 28PECh. 8.3 - Prob. 29PECh. 8.3 - Prob. 30PECh. 8.3 - Prob. 31PECh. 8.3 - Prob. 32PECh. 8.3 - Prob. 33PECh. 8.3 - Prob. 34PECh. 8.3 - Prob. 35PECh. 8.3 - Prob. 36PECh. 8.3 - Prob. 37PECh. 8.3 - Prob. 38PECh. 8.3 - Prob. 39PECh. 8.3 - Prob. 40PECh. 8.3 - Prob. 41PECh. 8.3 - Prob. 42PECh. 8.3 - Prob. 43PECh. 8.3 - Prob. 44PECh. 8.3 - Prob. 45PECh. 8.3 - Prob. 46PECh. 8.3 - Prob. 47PECh. 8.3 - Prob. 48PECh. 8.3 - Prob. 49PECh. 8.3 - Prob. 50PECh. 8.3 - Prob. 51PECh. 8.3 - Prob. 52PECh. 8.3 - Prob. 53PECh. 8.3 - Prob. 54PECh. 8.3 - Prob. 55PECh. 8.3 - Prob. 56PECh. 8.3 - Prob. 57PECh. 8.3 - Prob. 58PECh. 8.3 - Prob. 59PECh. 8.3 - Prob. 60PECh. 8.3 - Prob. 61PECh. 8.3 - The table gives an estimate of basic caloric needs...Ch. 8.3 - 63. Tire final grade in a particular course is...Ch. 8.3 - 64. Ina certain county, the proportion of voters...Ch. 8.3 - 65. What is ment by the order or a matrix? Give an...Ch. 8.3 - Prob. 66PECh. 8.3 - Prob. 67PECh. 8.3 - Prob. 68PECh. 8.3 - Prob. 69PECh. 8.3 - Prob. 70PECh. 8.3 - Prob. 71PECh. 8.3 - Prob. 72PECh. 8.3 - Prob. 73PECh. 8.3 - Prob. 74PECh. 8.3 - Prob. 75PECh. 8.3 - Prob. 76PECh. 8.3 - Prob. 77PECh. 8.3 - Prob. 78PECh. 8.3 - Prob. 79PECh. 8.3 - Prob. 80PECh. 8.3 - Prob. 81PECh. 8.3 - Prob. 82PECh. 8.3 - Prob. 83PECh. 8.3 - Prob. 84PECh. 8.3 - Prob. 85PECh. 8.3 - Prob. 86PECh. 8.3 - Prob. 87PECh. 8.3 - Prob. 88PECh. 8.3 - Prob. 89PECh. 8.3 - Prob. 90PECh. 8.3 - Prob. 91PECh. 8.3 - Prob. 1MCCPCh. 8.3 - Prob. 2MCCPCh. 8.3 - Prob. 3MCCPCh. 8.3 - Prob. 4MCCPCh. 8.3 - Prob. 5MCCPCh. 8.3 - Prob. 6MCCPCh. 8.3 - Prob. 7MCCPCh. 8.3 - Prob. 8MCCPCh. 8.3 - Prob. 9MCCPCh. 8.3 - Prob. 10MCCPCh. 8.4 - Check Point 1 Show that B is the multiplicative...Ch. 8.4 - Prob. 2CPCh. 8.4 - Check Point 3 Find the multiplicative inverse of...Ch. 8.4 - Prob. 4CPCh. 8.4 - Prob. 5CPCh. 8.4 - Prob. 6CPCh. 8.4 - Prob. 7CPCh. 8.4 - Prob. 1CVCCh. 8.4 - Prob. 2CVCCh. 8.4 - Prob. 3CVCCh. 8.4 - Prob. 4CVCCh. 8.4 - Prob. 5CVCCh. 8.4 - Prob. 6CVCCh. 8.4 - Prob. 7CVCCh. 8.4 - Prob. 8CVCCh. 8.4 - Prob. 9CVCCh. 8.4 - In Exercises 1-12, find the products AB and BA to...Ch. 8.4 - Prob. 2PECh. 8.4 - Prob. 3PECh. 8.4 - Prob. 4PECh. 8.4 - Prob. 5PECh. 8.4 - Prob. 6PECh. 8.4 - Prob. 7PECh. 8.4 - Prob. 8PECh. 8.4 - Prob. 9PECh. 8.4 - Prob. 10PECh. 8.4 - Prob. 11PECh. 8.4 - Prob. 12PECh. 8.4 - Prob. 13PECh. 8.4 - Prob. 14PECh. 8.4 - Prob. 15PECh. 8.4 - Prob. 16PECh. 8.4 - Prob. 17PECh. 8.4 - Prob. 18PECh. 8.4 - Prob. 19PECh. 8.4 - Prob. 20PECh. 8.4 - Prob. 21PECh. 8.4 - Prob. 22PECh. 8.4 - Prob. 23PECh. 8.4 - Prob. 24PECh. 8.4 - Prob. 25PECh. 8.4 - Prob. 26PECh. 8.4 - Prob. 27PECh. 8.4 - Prob. 28PECh. 8.4 - Prob. 29PECh. 8.4 - Prob. 30PECh. 8.4 - Prob. 31PECh. 8.4 - Prob. 32PECh. 8.4 - Prob. 33PECh. 8.4 - Prob. 34PECh. 8.4 - Prob. 35PECh. 8.4 - Prob. 36PECh. 8.4 - Prob. 37PECh. 8.4 - Prob. 38PECh. 8.4 - Prob. 39PECh. 8.4 - Prob. 40PECh. 8.4 - Prob. 41PECh. 8.4 - Prob. 42PECh. 8.4 - Prob. 43PECh. 8.4 - Prob. 44PECh. 8.4 - Prob. 45PECh. 8.4 - Prob. 46PECh. 8.4 - Prob. 47PECh. 8.4 - Prob. 48PECh. 8.4 - Prob. 49PECh. 8.4 - Prob. 50PECh. 8.4 - In Exercises 51-52, use the coding matrix A=[4131]...Ch. 8.4 - Prob. 52PECh. 8.4 - Prob. 53PECh. 8.4 - Prob. 54PECh. 8.4 - Prob. 55PECh. 8.4 - Prob. 56PECh. 8.4 - Prob. 57PECh. 8.4 - Prob. 58PECh. 8.4 - Prob. 59PECh. 8.4 - Prob. 60PECh. 8.4 - Prob. 61PECh. 8.4 - Prob. 62PECh. 8.4 - Prob. 63PECh. 8.4 - Prob. 64PECh. 8.4 - Prob. 65PECh. 8.4 - Prob. 66PECh. 8.4 - Prob. 67PECh. 8.4 - Prob. 68PECh. 8.4 - Prob. 69PECh. 8.4 - Prob. 70PECh. 8.4 - Prob. 71PECh. 8.4 - In Exercises 71-76, write each system in the form...Ch. 8.4 - Prob. 73PECh. 8.4 - Prob. 74PECh. 8.4 - Prob. 75PECh. 8.4 - Prob. 76PECh. 8.4 - Prob. 77PECh. 8.4 - Prob. 78PECh. 8.4 - Prob. 79PECh. 8.4 - Prob. 80PECh. 8.4 - Prob. 81PECh. 8.4 - I made an encoding error by selecting the wrong...Ch. 8.4 - Prob. 83PECh. 8.4 - Prob. 84PECh. 8.4 - Prob. 85PECh. 8.4 - Prob. 86PECh. 8.4 - Prob. 87PECh. 8.4 - Prob. 88PECh. 8.4 - 89. Give an example of a matrix that is its own...Ch. 8.4 - Prob. 90PECh. 8.4 - Prob. 91PECh. 8.4 - Prob. 92PECh. 8.4 - Prob. 93PECh. 8.4 - Prob. 94PECh. 8.4 - Prob. 95PECh. 8.4 - Prob. 96PECh. 8.4 - Prob. 97PECh. 8.4 - Prob. 98PECh. 8.4 - Prob. 99PECh. 8.5 - Prob. 1CPCh. 8.5 - Prob. 2CPCh. 8.5 - Prob. 3CPCh. 8.5 - Prob. 4CPCh. 8.5 - Prob. 5CPCh. 8.5 - Prob. 6CPCh. 8.5 - Prob. 1CVCCh. 8.5 - Prob. 2CVCCh. 8.5 - Prob. 3CVCCh. 8.5 - Prob. 4CVCCh. 8.5 - Prob. 5CVCCh. 8.5 - Prob. 1PECh. 8.5 - Prob. 2PECh. 8.5 - Prob. 3PECh. 8.5 - Prob. 4PECh. 8.5 - Prob. 5PECh. 8.5 - Prob. 6PECh. 8.5 - Prob. 7PECh. 8.5 - Prob. 8PECh. 8.5 - Prob. 9PECh. 8.5 - Prob. 10PECh. 8.5 - Prob. 11PECh. 8.5 - Prob. 12PECh. 8.5 - Prob. 13PECh. 8.5 - Prob. 14PECh. 8.5 - Prob. 15PECh. 8.5 - Prob. 16PECh. 8.5 - Prob. 17PECh. 8.5 - Prob. 18PECh. 8.5 - Prob. 19PECh. 8.5 - Prob. 20PECh. 8.5 - Prob. 21PECh. 8.5 - Prob. 22PECh. 8.5 - Prob. 23PECh. 8.5 - Prob. 24PECh. 8.5 - Prob. 25PECh. 8.5 - Prob. 26PECh. 8.5 - Prob. 27PECh. 8.5 - Prob. 28PECh. 8.5 - Prob. 29PECh. 8.5 - Prob. 30PECh. 8.5 - Prob. 31PECh. 8.5 - Prob. 32PECh. 8.5 - In Exercises 29-36, use Cramer's Rule to solve...Ch. 8.5 - Prob. 34PECh. 8.5 - Prob. 35PECh. 8.5 - Prob. 36PECh. 8.5 - Prob. 37PECh. 8.5 - Prob. 38PECh. 8.5 - Prob. 39PECh. 8.5 - Prob. 40PECh. 8.5 - Prob. 41PECh. 8.5 - Prob. 42PECh. 8.5 - Prob. 43PECh. 8.5 - Prob. 44PECh. 8.5 - Prob. 45PECh. 8.5 - Prob. 46PECh. 8.5 - Prob. 47PECh. 8.5 - Prob. 48PECh. 8.5 - Prob. 49PECh. 8.5 - Prob. 50PECh. 8.5 - Prob. 51PECh. 8.5 - then the points ,and are collinear. If the...Ch. 8.5 - Prob. 53PECh. 8.5 - Prob. 54PECh. 8.5 - Prob. 55PECh. 8.5 - Prob. 56PECh. 8.5 - Prob. 57PECh. 8.5 - Prob. 58PECh. 8.5 - Prob. 59PECh. 8.5 - Prob. 60PECh. 8.5 - Prob. 61PECh. 8.5 - 62. If you could use only one method to solve...Ch. 8.5 - Use the feature of your graphing utility that...Ch. 8.5 - Prob. 64PECh. 8.5 - Prob. 65PECh. 8.5 - Prob. 66PECh. 8.5 - Prob. 67PECh. 8.5 - Prob. 68PECh. 8.5 - Prob. 69PECh. 8.5 - Prob. 70PECh. 8.5 - Prob. 71PECh. 8.5 - Prob. 72PECh. 8.5 - Prob. 73PECh. 8.5 - Prob. 74PECh. 8.5 - 75. Show that the equation of a line through and ...Ch. 8.5 - Prob. 76PECh. 8.5 - Prob. 77PECh. 8.5 - Prob. 78PECh. 8.5 - Prob. 79PECh. 8.5 - Prob. 80PECh. 8.5 - Prob. 81PECh. 8.5 - Prob. 82PECh. 8.5 - Prob. 83PECh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - Prob. 7TCh. 8 - Prob. 8TCh. 8 - Prob. 9TCh. 8 - Prob. 10TCh. 8 - Prob. 1CRECh. 8 - Prob. 2CRECh. 8 - Prob. 3CRECh. 8 - Prob. 4CRECh. 8 - Solve each equation or inequality in Exercises...Ch. 8 - Prob. 6CRECh. 8 - Prob. 7CRECh. 8 - Prob. 8CRECh. 8 - Prob. 9CRECh. 8 - Prob. 10CRECh. 8 - Prob. 11CRECh. 8 - Prob. 12CRECh. 8 - Prob. 13CRECh. 8 - Prob. 14CRECh. 8 - Prob. 15CRECh. 8 - Prob. 16CRECh. 8 - Prob. 17CRECh. 8 - Prob. 18CRECh. 8 - Prob. 19CRECh. 8 - Prob. 20CRECh. 8 - Prob. 21CRECh. 8 - Prob. 22CRECh. 8 - Prob. 23CRECh. 8 - Prob. 24CRECh. 8 - Prob. 25CRE
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- 1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$arrow_forward3 Evaluate the double integral 10 y√x dy dx. First sketch the area of the integral involved, then carry out the integral in both ways, first over x and next over y, and vice versa.arrow_forwardQuestion 2. i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) = P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer. ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer.arrow_forward
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