#55 0.621. 0.7-0.3]0.10.2 0.322. -0.30.243. A-B---10.20.2-0.90.50.50.-4644. A -0B--2423. 3224. 324434555 5Ce tcer et dy C72Chapter 2 MatricesSolving a System of Equations Using an InverseIn Exercises 45-48, use an inverse matrix to solve eachsystem of linear equations.Singular Matrix In Exercises 55 and 56, find x suchthat the matrix is singular..55. A -[-56. A -46. (a) 2x - y- -32r +y= 745. (a) x+ 2y --x- 2y - 3Solving a Matrix Equation In Exercises 57 and 58,find A.(b) x+ 2y - 10(b) 2x - y--Ix- 2y - -62x +y--357. (24)- -58. (44)- -47. (a) x, + 2x, + x,- 2X + 2x, - - 4X - 2x, + --2(b) x, + 2x, + x,- IX, + 2x, - x,- 3X- 2x, + x, --348. (a) x, + X, - 2x, - 0X- 2x, + x - 0X,- X,- x,--1(b) x, + x - 2x, - -I,- 2x, + , - 2Finding the Inverse of a Matrix In Exercises 59and 60, show that the matrix is invertible and find itsinverse.59, a - [-[sec e tan esin e co f|- cos 6sin e 60. Asin eItan e sec eBeam Deflection In Exercises 61 and 62, forces w.Wand w, (in pounds) act on a simply supported elasticbeam, resulting in deflections d, dz, and d, (in inches) inthe beam (see figure).Solving a System of Equations Using an InverseIn Exercises 49-52, use a software program or agraphing utility to solve the system of linear equationsusing an inverse matrix.49. X, + 2x, - , + 3x, - --3X - 3x, + x, + 2x, - X = -32r, + x + 1, - 3x, + x, = 6X- + 2x, + -X= 22x, + -A + 2x, + X- -3Use the matrix equation d- Fw, where--Ed =50. , + x - x, + 3x, - x, - 32x, + 1 + + + I = 4X, + X - x + 2x,- x,- 32x, +x, + 4x, + x- x, - -13x, +x+ - 2, + x- 551. 2r, - 3x, + x - 2, + Xg - 4xg = 203x, + - 4x, + - + 2x,-- 164x, + - 3x, + 4, - + 2,- -12-Sx, - + 4x, + 2x, - 5x, + 3x, -2X+ - 3x,+ 4 - 3x, + X--153x, - X + 2x, - 3x, + 2r, - 6r, - 254x, - 2x, + 4x, + 2, - Sx, - - I3x, + 6x, - Sx, - 6, + 3x, + 3x,- -112x, - 3x, + x, + 3, - - 2, 0-X, + 4x, - 4x, - 6, + 2x, + 4x,- -93x, - , + Sx, + 2x, - 3x,- 2r, + 3x, - 4x, - 6x, + x, + 2x, - - 12and Fis the 3 x 3 flexibility matrix for the beam, to findthe stiffness matrix F- and the force matrix w. Theentries of F are measured in inches per pound.0.008 0.004 0.00361. F-0.004 0.006 0.0040.003 0.004 0.008[0.017 0.010 0.00862. F= 0.010 0.012 0.010. d =0.150.008 0.010 0.017][0.585d-0.6400.835[ 0]of63. Proof Prove Property 2 of Theorem 2.8: If A is aninvertible matrix and is a positive integer, then52.(A)- - A'A-. A- (A-Yk factors5x, - I64. Proof Prove Property 4 of Theorem 2.8: If A is aninvertible matrix, then (A)-- (A-.65. Proof Prove Property 2 of Theorem 2.10: If C is aninvertible matrix such that CA - CB, then A - B.66. Proof Prove that if A= A, thenMatrix Equal to Its Own Inverse In Exercises 53 and54, find r such that the matrix is equal to its own inverse.53. A -|54. A-i1- 24 = (1 - 24)-1.C Cm ey m C l2.3 Exercises7367. Guided Proof Prove that the inverse of a symmetricnonsingular matrix is symmetric.Getting Started: To prove that the inverse of A issymmetric, you need to show that (A-)7 = A-.(i) Let A be a symmetric, nonsingular matrix.(ii) This means that A = A and A exists.75. Use the result of Exercise 74 to find A for eachmatrix.[-1(a) A-30 02(iii) Use the properties of the transpose to show that(A- is equal to A.(b) A =068. Proof Prove that if A, B, and C are square matricesand ABC = 1, then B is invertible and B- CA.76. Let A=69. Proof Prove that if A is invertible and AB - 0,then B = 0.70. Guided Proof Prove that if A - A, then either A issingular or A-.(a) Show that A - 24 + 51 - O, where I is theidentity matrix of order 2.(b) Show that A-- (21 - A).(c) Show that for any square matrix satisfyingA - 24 + 5/- 0, the inverse of A isGetting Started: You must show that either A is singularor A equals the identity matrix.(i) Begin your proof by observing that A is eithersingular or nonsingular.A-- (21 - A).77. Proof Let u be an nxI column matrix satisfyingu'u - . The x matrix H - 1, - 2uu' is called aHouseholder matrix.(ii) If A is singular, then you are done.(ii) If A is nonsingular, then use the inverse matrix A-and the hypothesis A A to show thatA-/(a) Prove that H is symmetric and nonsingular.True or False? In Exercises 71 and 72, determinewhether each statement is true or false. If a statement(b) Let u =2/2 Show that u'u = 1, and find theis true, give a reason or cite an appropriate statementfrom the text. If a statement is false, provide an examplHouscholder matrix H

Name: #55 0.621. 0.7-0.3]0.10.2 0.322. -0.30.243. A-B---10.20.2-0.90.50.50.-
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #55 0.621. 0.7-0.3]0.10.2 0.322. -0.30.243. A-B---10.20.2-0.90.50.50.-4644. A -0B--2423. 3224. 324434555 5Ce tcer et dy C72Chapter 2 MatricesSolving a System of Equations Using an InverseIn Exercises 45-48, use an inverse matrix to solve eachsystem o

For (55), We are given the matrix A=4x-2-3. Here, we need to find x such that the matrix is…

Answered: Singular Matrix In Exercises 55 and 56,…

Math

Algebra

Singular Matrix In Exercises 55 and 56, find z such that the matrix is singular. 55. A - 56. A --

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: z'dz 214

A: We have to find ∫x2 dxx3+4.

Q: Find L{1}ℒ{1}.

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 5(18)

A: To find5(18)

Q: 4x 3x + 4 5x

A: In a parallelogram diagonals bisect each other.

Q: 7/2 + 3 4/6

Q: %3D n+1 3 -2 -3

Q: こ (0) of

Q: 196. 2(n+1)

Q: 3/4 5/6

A: The given set of questions , 1 13÷16 Apply division rule , 1316=13×61 =2 2 25÷47 Apply…

Q: (4 – a2)

A: To integrate.

Q: -8 - 12

A: Given problem is

Q: 3/8+5/24

A: The given expression is 3/8 + 5/24.Simplify the given expression as follows.

Q: 5/3 divied 5/2

Q: A large speaker that you are planning to use, has a huge diaphragm connected to a spring, the force…

Q: In the

A: In the diagram it is given that, the angles <G and <H are complementary. m<G = 2x + 10…

Q: edxte*

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T. r…

A: We will evaluate the required value.

Q: 2. 9=x-2y 3x + 5 = 2y

A: The given equations are system of linear equations in variables x and y. We solve these by…

Q: 2426

A: Given expression: 2+2

Q: (24) Half the product of a number t and 48

A: The objective is to half the product of a number t and 48.

Q: 4 1/2 + 3 2/3=

A: Given,

Q: Number 6.12

A: From part (6.11), Let x be the random variable denote that the amount of snow fall between 1 inch…

Q: 6. Using the data from the contingency table, obtain the value of the test statistic of our test. 7.…

A: Step 1: Given: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored…

Q: 2.763-4.5(2.1x-5.1432)=6.32x+5

Q: 2/5 +7/12

A: Please see the answer below.

Q: -2 -4 and D = 4 8

Q: -2.2p

A: -2. 2p = (-2) (2p) = -4p

Q: -(2/5)-3

Q: 8 15 2 15

A: 8/15 -2/15 here simple substraction given and fraction is given calculation is given inbelow

Q: (NINETEEN)

A: The information provided in the are as follows :-Level of significance

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

100%

#55

0.6
21. 0.7
-0.3]
0.1
0.2 0.3
22. -0.3
0.2
43. A-
B--
-1
0.2
0.2
-0.9
0.5
0.5
0.
-4
6
44. A -0
B--2
4
23. 3
2
24. 3
2
4
4
3
4
5
5
5 5
Ce tcer e
t dy C
72
Chapter 2 Matrices
Solving a System of Equations Using an Inverse
In Exercises 45-48, use an inverse matrix to solve each
system of linear equations.
Singular Matrix In Exercises 55 and 56, find x such
that the matrix is singular.
.
55. A -[-
56. A -
46. (a) 2x - y- -3
2r +y= 7
45. (a) x+ 2y --
x- 2y - 3
Solving a Matrix Equation In Exercises 57 and 58,
find A.
(b) x+ 2y - 10
(b) 2x - y--I
x- 2y - -6
2x +y--3
57. (24)- -
58. (44)- -
47. (a) x, + 2x, + x,- 2
X + 2x, - - 4
X - 2x, + --2
(b) x, + 2x, + x,- I
X, + 2x, - x,- 3
X- 2x, + x, --3
48. (a) x, + X, - 2x, - 0
X- 2x, + x - 0
X,- X,- x,--1
(b) x, + x - 2x, - -I
,- 2x, + , - 2
Finding the Inverse of a Matrix In Exercises 59
and 60, show that the matrix is invertible and find its
inverse.
59, a - [-
[sec e tan e
sin e co f
|- cos 6
sin e 60. A
sin e
I
tan e sec e
Beam Deflection In Exercises 61 and 62, forces w.W
and w, (in pounds) act on a simply supported elastic
beam, resulting in deflections d, dz, and d, (in inches) in
the beam (see figure).
Solving a System of Equations Using an Inverse
In Exercises 49-52, use a software program or a
graphing utility to solve the system of linear equations
using an inverse matrix.
49. X, + 2x, - , + 3x, - --3
X - 3x, + x, + 2x, - X = -3
2r, + x + 1, - 3x, + x, = 6
X- + 2x, + -X= 2
2x, + -A + 2x, + X- -3
Use the matrix equation d- Fw, where
--E
d =
50. , + x - x, + 3x, - x, - 3
2x, + 1 + + + I = 4
X, + X - x + 2x,- x,- 3
2x, +x, + 4x, + x- x, - -1
3x, +x+ - 2, + x- 5
51. 2r, - 3x, + x - 2, + Xg - 4xg = 20
3x, + - 4x, + - + 2x,-- 16
4x, + - 3x, + 4, - + 2,- -12
-Sx, - + 4x, + 2x, - 5x, + 3x, -2
X+ - 3x,+ 4 - 3x, + X--15
3x, - X + 2x, - 3x, + 2r, - 6r, - 25
4x, - 2x, + 4x, + 2, - Sx, - - I
3x, + 6x, - Sx, - 6, + 3x, + 3x,- -11
2x, - 3x, + x, + 3, - - 2, 0
-X, + 4x, - 4x, - 6, + 2x, + 4x,- -9
3x, - , + Sx, + 2x, - 3x,
- 2r, + 3x, - 4x, - 6x, + x, + 2x, - - 12
and Fis the 3 x 3 flexibility matrix for the beam, to find
the stiffness matrix F- and the force matrix w. The
entries of F are measured in inches per pound.
0.008 0.004 0.003
61. F-0.004 0.006 0.004
0.003 0.004 0.008
[0.017 0.010 0.008
62. F= 0.010 0.012 0.010. d =0.15
0.008 0.010 0.017]
[0.585
d-0.640
0.835
[ 0]
of
63. Proof Prove Property 2 of Theorem 2.8: If A is an
invertible matrix and is a positive integer, then
52.
(A)- - A'A-. A- (A-Y
k factors
5x, - I
64. Proof Prove Property 4 of Theorem 2.8: If A is an
invertible matrix, then (A)-- (A-.
65. Proof Prove Property 2 of Theorem 2.10: If C is an
invertible matrix such that CA - CB, then A - B.
66. Proof Prove that if A= A, then
Matrix Equal to Its Own Inverse In Exercises 53 and
54, find r such that the matrix is equal to its own inverse.
53. A -|
54. A-i
1- 24 = (1 - 24)-1.
C Cm e
y m C l
2.3 Exercises
73
67. Guided Proof Prove that the inverse of a symmetric
nonsingular matrix is symmetric.
Getting Started: To prove that the inverse of A is
symmetric, you need to show that (A-)7 = A-.
(i) Let A be a symmetric, nonsingular matrix.
(ii) This means that A = A and A exists.
75. Use the result of Exercise 74 to find A for each
matrix.
[-1
(a) A-
3
0 0
2
(iii) Use the properties of the transpose to show that
(A- is equal to A.
(b) A =0
68. Proof Prove that if A, B, and C are square matrices
and ABC = 1, then B is invertible and B- CA.
76. Let A=
69. Proof Prove that if A is invertible and AB - 0,
then B = 0.
70. Guided Proof Prove that if A - A, then either A is
singular or A-.
(a) Show that A - 24 + 51 - O, where I is the
identity matrix of order 2.
(b) Show that A-- (21 - A).
(c) Show that for any square matrix satisfying
A - 24 + 5/- 0, the inverse of A is
Getting Started: You must show that either A is singular
or A equals the identity matrix.
(i) Begin your proof by observing that A is either
singular or nonsingular.
A-- (21 - A).
77. Proof Let u be an nxI column matrix satisfying
u'u - . The x matrix H - 1, - 2uu' is called a
Householder matrix.
(ii) If A is singular, then you are done.
(ii) If A is nonsingular, then use the inverse matrix A-
and the hypothesis A A to show thatA-/
(a) Prove that H is symmetric and nonsingular.
True or False? In Exercises 71 and 72, determine
whether each statement is true or false. If a statement
(b) Let u =2/2 Show that u'u = 1, and find the
is true, give a reason or cite an appropriate statement
from the text. If a statement is false, provide an exampl
Houscholder matrix H

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.