Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
9th Edition
ISBN: 9780321962218
Author: Steven J. Leon
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 1.2, Problem 13E
Given a homogeneous system of linear equations, if the system is overdetermined, what are the possibilities as to the number of solutions? Explain.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Co Given
show that
Solution
Take home
Су-15
1994
+19
09/2
4
=a
log
суто
-
1092
ж
= a-1
2+1+8
AI | SHOT ON S4
INFINIX CAMERA
a
Question 7. If det d e f
ghi
V3
= 2. Find det
-1
2
Question 8. Let A = 1
4
5
0
3
2.
1 Find adj (A)
2 Find det (A)
3
Find A-1
2g 2h 2i
-e-f
-d
273
2a 2b 2c
Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 1 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
Ch. 1.1 - Use back substitution to solve each of the...Ch. 1.1 - Write out the coefficient matrix for each of the...Ch. 1.1 - In each of the following systems, interpret each...Ch. 1.1 - Write an augmented matrix for each of the systems...Ch. 1.1 - Write out the system of equations that corresponds...Ch. 1.1 - Solve each of the following systems. (a)...Ch. 1.1 - The two systems 2x1+x2=34x1+3x2=5 and...Ch. 1.1 - Solve the two systems...Ch. 1.1 - Given a System of the form m1x1+x2=b1m2x1+x2=b2...Ch. 1.1 - Consider a system of the form...
Ch. 1.1 - Give a geometrical interpretation of a linear...Ch. 1.2 - Which of the matrices that follow are in row...Ch. 1.2 - The augmented matrices that follow are in row...Ch. 1.2 - The augmented matrices that follow are in reduced...Ch. 1.2 - For each of the systems in Exercise 3, make a list...Ch. 1.2 - For each of the systems of equations that follow,...Ch. 1.2 - Use GaussJordan reduction to solve each of the...Ch. 1.2 - Give a geometric explanation of why a homogeneous...Ch. 1.2 - Consider a linear system whose augmented matrix is...Ch. 1.2 - Consider a linear system whose augmented matrix is...Ch. 1.2 - Consider a linear system whose augmented matrix is...Ch. 1.2 - Given the linear systems...Ch. 1.2 - Given the linear systems (i)...Ch. 1.2 - Given a homogeneous system of linear equations, if...Ch. 1.2 - Given a nonhomogeneous system of linear equations,...Ch. 1.2 - Determine the values ofx1,x2,x3,x4for the...Ch. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - In Application 3 the solution (6, 6, 6, 1) was...Ch. 1.2 - Prob. 19ECh. 1.2 - Nitric acid is prepared commercially by a series...Ch. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.3 - If A=[314201122]andB=[102311241] compute (a) 2A...Ch. 1.3 - For each of the pairs of matrices that follow,...Ch. 1.3 - For which of the pairs in Exercise 2 is it...Ch. 1.3 - Write each of the following systems of equations...Ch. 1.3 - If A=[341127] verify that (a) 5A=3A+2A (b)...Ch. 1.3 - If A=[ 4 2 1 3 6 5 ]andB=[ 1 2 3 2 2 4 ] verify...Ch. 1.3 - If A=[216324]andB=[2416] verify that (a)...Ch. 1.3 - If A=[ 2 1 4 3 ],B=[ 2 0 1 4 ],C=[ 3 2 1 1 ]...Ch. 1.3 - Let A=[ 1 1 2 2 ],b=[40],c=[32] (a) Write b as a...Ch. 1.3 - For each of the choices of A and b that follow,...Ch. 1.3 - Let Abe a 53 matrix. If b=a1+a2=a2+a3 then what...Ch. 1.3 - Let Abe a 34 matrix. If b=a1+a2+a3+a4 then what...Ch. 1.3 - Let Ax=b be a linear system whose augmented matrix...Ch. 1.3 - Prob. 14ECh. 1.3 - Let A be an mn matrix. Explain why the matrix...Ch. 1.3 - A matrix A is said to be skew symmetric if AT=A ....Ch. 1.3 - In Application 3, suppose that we are searching...Ch. 1.3 - Let A be a 22 matrix with a110 and let =a21/a11 ....Ch. 1.4 - Explain why each of the following algebraic rules...Ch. 1.4 - Will the rules in Exercise 1 work if a is replaced...Ch. 1.4 - Find nonzero 22 matrices A and B such that AB=0 .Ch. 1.4 - Find nonzero matrices A, B, and C such that...Ch. 1.4 - The matrix A=[1111] has the property that A2=O ....Ch. 1.4 - Prove the associative law of multiplication for 22...Ch. 1.4 - Let A=[ 1 2 1 2 1 2 1 2] Compute A2 and A3 . What...Ch. 1.4 - Let A=[ 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1...Ch. 1.4 - Let A=[0100001000010000] Show that An=O for n4 .Ch. 1.4 - Let A and B be symmetric nn matrices. For each of...Ch. 1.4 - Let C be nonsymmetric nn matrix. For each of the...Ch. 1.4 - Let A=[ a 11 a 12 a 21 a 22] Show that if...Ch. 1.4 - Use the result from Exercise 12 to find the...Ch. 1.4 - Let A and B are nn matrices. Show that if...Ch. 1.4 - Let A be a nonsingular matrix. Show that A1 is...Ch. 1.4 - Prove that if A is nonsingular then AT is...Ch. 1.4 - Let A be an nn matrix and let x and y be vectors...Ch. 1.4 - Let A be a nonsingular nn matrix. Use mathematical...Ch. 1.4 - Let A be an nn matrix. Show that if A2=O , then IA...Ch. 1.4 - Let A be an nn matrix. Show that if Ak+1=O , then...Ch. 1.4 - Given R=[cossinsincos] Show that R is nonsingular...Ch. 1.4 - An nn matrix A is said to be an involutionifA2=I ....Ch. 1.4 - Let u be a unity vector in n (i.e. uTu=1 ) and let...Ch. 1.4 - A matrix A is said to be an idempotentif A2=A ....Ch. 1.4 - Prob. 25ECh. 1.4 - Let D be an nn diagonal matrix whose diagonal...Ch. 1.4 - Let Abe an involution matrix and let...Ch. 1.4 - Let A be an mn matrix. Show that ATA and AAT are...Ch. 1.4 - Let A and B be symmetric nn matrices. Prove that...Ch. 1.4 - Let Abe an nn matrix and let B=A+ATandC=AAT (a)...Ch. 1.4 - In Application 1, how many married women and how...Ch. 1.4 - Consider the matrix A=[ 0 1 0 1 1 1 0 1 1 0 0 1 0...Ch. 1.4 - Consider the graph (a) Determine the adjacency...Ch. 1.4 - If Ax=Bx for some nonzero vector x, then the...Ch. 1.4 - If A and B are singular nn matrices, then A+B is...Ch. 1.4 - If A and B are nonsingular matrices, then (AB)T is...Ch. 1.5 - Which of the matrices that follow are elementary...Ch. 1.5 - Find the inverse of each matrix in Exercise 1. For...Ch. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Let A=[ 1 2 1 2 1 0 4 3 2 ],B=[ 1 2 2 2 1 2 4 3 6...Ch. 1.5 - Prob. 6ECh. 1.5 - Let A=[2164] (a) Express A1 as a product of...Ch. 1.5 - Compute the LU factorization of each of the...Ch. 1.5 - Let A=[ 1 3 2 0 3 2 1 4 3 ] (a) Verify that A1=[ 1...Ch. 1.5 - Find the inverse of each of the following...Ch. 1.5 - Prob. 11ECh. 1.5 - Let A=[ 5 3 3 2 ],B=[ 6 2 2 4 ],C=[ 4 6 2 3 ]...Ch. 1.5 - Is the transpose of an elementary matrix an...Ch. 1.5 - Let U and R bennupper triangular matrices and...Ch. 1.5 - Let A be a 33 matrix and suppose that 2a1+a24a3=0...Ch. 1.5 - Prob. 16ECh. 1.5 - Let A and B be nn matrices and let C=AB . Show...Ch. 1.5 - Prob. 18ECh. 1.5 - Let U be an nn upper triangular matrix with...Ch. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Show that if A is a symmetric nonsingular matrix...Ch. 1.5 - Prove that if A is a row equivalent to B then B is...Ch. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prove that B is row equivalent to A if and only if...Ch. 1.5 - Is it possible for a singular matrix B to be row...Ch. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.6 - Let A be a nonsingular nn matrix. Perform the...Ch. 1.6 - Prob. 2ECh. 1.6 - Let A=[ 1 2 1 1 ]andB=[ 2 1 1 3 ] (a) Calculate...Ch. 1.6 - Let I=[ 1 0 0 1 ],E=[ 0 1 1 0 ],O=[ 0 0 0 0 ] C=[...Ch. 1.6 - Perform each of the following block...Ch. 1.6 - Given X=[ 2 4 1 2 5 3 ],Y=[ 1 2 2 3 4 1 ] (a)...Ch. 1.6 - Let A=[ A 11 A 21 A 12 A 22 ]andAT=[ A 11 T A 12 T...Ch. 1.6 - Let Abe an mn matrix, X and nr matrix, and B an mn...Ch. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Let A and B be nn matrices and let M be a block...Ch. 1.6 - Prob. 13ECh. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Let A, B, L, M, S, and T be nn matrices with A, B,...Ch. 1.6 - Let Abe an nn matrix and xn . (a) A scalar c can...Ch. 1.6 - If A is an nn matrix with the property that Ax=0...Ch. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1 - Use MATLAB to generate random 44 matrices A and B....Ch. 1 - Set n=200 and generate an nn matrix and two...Ch. 1 - Set A=floor(10*rand(6)) . By construction, the...Ch. 1 - Construct a mainx as follows: Set...Ch. 1 - Generate a matrix A by setting A = floor(10 *...Ch. 1 - Consider the graph (a) Determine the adjacency...Ch. 1 - In Application 1 of Section 1.4, the numbers of...Ch. 1 - The following table describes a seven-stage model...Ch. 1 - Set A = magic(8) and then compute its reduced row...Ch. 1 - Set B=[1,1;1,1] and A=[zeros(2),eye(2);eye(2),B]...Ch. 1 - The MATLAB commands A = floor(10 * rand((6)), B=AA...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - This chapter test consists of trueorfalse...Ch. 1 - Find all solutions of the linear system...Ch. 1 - (a) A linear equation in two unknowns corresponds...Ch. 1 - LetAx=bbe a system of n linear equations in n...Ch. 1 - LetAbeamatrix of the form A=[22] where and are...Ch. 1 - Let A=[213427135],B=[213135427],C=[013027535] Find...Ch. 1 - Let A be a 33 matrix and let b=3a1+a2+4a3 Will the...Ch. 1 - Let A be a 33 matrix and suppose that a13a2+2a3=0...Ch. 1 - Given the vector x0=[11] is it possible to find 22...Ch. 1 - Let A and B be symmetric nn matrices and let C=AB...Ch. 1 - Let E and F be nn elementary matrices and let C=EF...Ch. 1 - Given A=[IOOOIOOBI] where all the submatrices are...Ch. 1 - LetA and B be 1010 matrices that are...
Additional Math Textbook Solutions
Find more solutions based on key concepts
1. How much money is Joe earning when he’s 30?
Pathways To Math Literacy (looseleaf)
23. A plant nursery sells two sizes of oak trees to landscapers. Large trees cost the nursery $120 from the gro...
College Algebra (Collegiate Math)
CHECK POINT I Consider the six jokes about books by Groucho Marx. Bob Blitzer. Steven Wright, HennyYoungman. Je...
Thinking Mathematically (6th Edition)
Provide an example of a qualitative variable and an example of a quantitative variable.
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
The first derivative of function y=25x4.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
(a) Make a stem-and-leaf plot for these 24 observations on the number of customers who used a down-town CitiBan...
APPLIED STAT.IN BUS.+ECONOMICS
Knowledge Booster
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.Similar questions
- Question 5. Let A, B, C ben x n-matrices, S is nonsigular. If A = S-1 BS, show that det (A) = det (B) Question 6. For what values of k is the matrix A = (2- k -1 -1 2) singular? karrow_forward1 4 5 Question 3. Find A-1 (if exists), where A = -3 -1 -2 2 3 4 Question 4. State 4 equivalent conditions for a matrix A to be nonsingulararrow_forwardHow long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)arrow_forward
- Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forwardConsider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forward
- Question 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forwardAssume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forward
- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
UG/ linear equation in linear algebra; Author: The Gate Academy;https://www.youtube.com/watch?v=aN5ezoOXX5A;License: Standard YouTube License, CC-BY
System of Linear Equations-I; Author: IIT Roorkee July 2018;https://www.youtube.com/watch?v=HOXWRNuH3BE;License: Standard YouTube License, CC-BY