ERRATA for PRINTING 2 of the 10th Edition 12/28/11

Unless noted otherwise, the following corrections apply to the second printings of both Elementary Linear Algebra, 10th Edition (ELA) and Elementary Linear Algebra with Applications 10th Edition, (ELA+Apps). The printing number is the rightmost digit at the bottom of the copyright page in the front matter.

Page 9, Exercises 7 and 8
Change the word “vector” to “3-tuple”
Page 24, Exercise 40a
Change the start of the sentence to read, “If A is a matrix with three rows and five columns, then, …”
Page 24, Exercise 40b
Change the start of the sentence to read, “If B is a matrix with three rows and six columns, then, …”
Page 24, Exercise 40c
Change the start of the sentence to read, “If C is a matrix with five rows and three columns, then, …”
Page 49, Exercises 20 and 21
Change the problem statement to read, “Repeat parts (a), (c), (d), (e), and (f) of Exercise 18 for the matrix”
Page 66, part (b) of the True/False
Change the first part of the sentence to read, “If A is a square matrix, and if the linear system Ax = b has a unique solution, then…”
Page 69, second displayed formula
In the second grouping, change the first term to read, “aijbjj”
Page 95, first text line below display (4)
Change “det[A]” to “det(A)”
Page 97, Title of Example 6
Change title to read, “Determinant of a Lower Triangular Matrix”, and near the end of the first text line of Example 6, chance “upper triangular” to “lower triangular”
Page 99, direction line for Exercises 5-8
Reference should be to Equation (2)
Page 102, first displayed formula
Following the first = sign in the display, change the expression “ka33C13” to read “ka13C13”, and following the second = sign change the expression “a33C13” to read “a13C13”
Page 110, margin note
Move the margin note to the bottom of p.111, and change the first two lines to read, “It follows from Theorems 2.3.5 and 2.1.2 that if A is an invertible triangular matrix, then…
Page 127, last line of Definition 4
Change the word “XXXultiple” to read “multiple”
Page 129, first line of Exercise 11
Change line to read, “Find an initial point P of a nonzero vector u = PQ with terminal point Q(3, 0, –5) and such that”. [Put a vector bar on top of PQ]
Page 129, first line of Exercise 12
Change the line to read, “Find a terminal point Q of a nonzero vector u = PQ with initial point P(–1, 3, –5) and such that”. [Put a vector bar on top of PQ]
Page 129, first part of Exercise 16
Change text to read, “Let v and w be the vectors in Exercise 15. Find…”
Page 138, Theorem 3.2.5 has extraneous hypothesis
Change the theorem hypotheses to read: “If u, v, and w are vectors in Rn, then:”
Page 147, Figure 3.3.3
Change the label of the dot on the line L to read, “(cos
Page 150 Concept Review
Add the bulleted item “Orthonormal set of vectors”
Page 153 last line before Theorem 3.4.2
Change the last sentence to read, “In summary, we have the following result.”
Page 213, last line of Proof (c)
Change “dim(W) = dim(V)” to read: “W = V”
Page 257, Table 8
Change the parenthetical equation in the upper left white box to read, “”
Page 257, Table 8
Change the parenthetical equation in the lower left white box to read, “(k > 1)”
Page 259, end of the second line of the statement of Example 6
Change to read, “…with the positive x-axis.”
Page 260: First line of the statement of Example 7
Change the first part of the line to read, “Find the reflection of the vector x =(1, 5) about the line …”
Page 262, Exercise 28c
Change the problem to read, “Find all solutions of the equation in Exercise 27 that lie in the interval [0, 2, and then by substituting those solutions in Formula (15), find an angle of rotation about the axis in part (b) that results from multiplication by the matrix A in part (a).”
P270: First displayed equation on the page
Change reference number to “(10)”
P274, line following display (1)
Change text to read, “This shows that multiplication by a diagonal 2 x 2 matrix with nonnegative entries compresses or expands the…”
P275, 5th line of table (not counting headings)
Matrix should be
P275, 6th line of table (not counting headings)
Matrix should be
P275, 7th line of the table (not counting headings)
The label on the dot on the right part of the figure should be (1 + k, 1)
P275, 8th line of table (not counting headings)
Change the text in the leftmost box to read, “Shear in the y-direction with factor k > 0”, and change the right part of the figure to be a parallelogram with vertices (0, 0), (0, 1),
(1, 1+ k), (1, k)
Page 280, lead in to Exercise 9
Change text to read, “Find the 2 x 2 matrix that shears by”
Page 280, lead in to Exercise 10
Change text to read, “Find the 2 x 2 matrix that compresses or expands by”
Page 281, lead in to Exercise 13 and to Exercise 14
Change the text to read, “In each part, find a single 2 x 2 matrix that performs…”
Page 284, first sentence of the last paragraph
The words, “state vector” in that sentence should be set boldface, italic.
Page 296, Figure 5.1.1
The second legend should read, “
P 305, second line following Definition 1
Change “express B as B = Q–1AQ” to read “express A as A = Q–1BQ”
Page 307, last displayed formula at the end of Example 1
In second matrix, change the last entry in the first column from “21” to “1”
P311, second display in Example 6
Change the second equation to read, rather than
Page 329, Solution (c), first text line after the block of three displayed formulas
Fix to read: “so the solution satisfying these conditions is”
Page 349, line immediately above Theorem 6.2.5
Reference should read “4.8.8” rather than “6.2.5”
Page 362, Theorem 6.3.8, second displayed formula
There should be primes on vs+1 and vk
Page 365, Exercise 18,
The third line should be changed to read “…radians with the positive x-axis. Solve that”
Page 396, Exercise 15(a)
Change the last two lines to read: “…is either a rotation or a reflection followed by a rotation.”
Page 396, Exercise 16
Change the second and third lines of the statement to read: “…is a rotation or a reflection followed by a rotation. Find the angle of rotation in either case.”
Page 404 Exercise 19, last sentence
“you” should read “your”
Page 404, Exercise 20, formula for A
The coefficient “c” should read “c1”
Page 405, Theorem 7.2.4
Change the first line to read, “If A is an nn matrix with real entries, then …”
P409: Replace the line immediately following Formula (11) with:
“If a, b, and c are not all zero, then the graphs of these equations in R3 are called central quadrics and, more specifically, the graph of the second equation is called a central quadric in standard position.”
Page 434, the marginal note should read:
“T(–v) = –T(v)”
Page 438, second displayed formula in Example 11
Change the display to read,
“D(f + g) = D(f) + D(g) and D(kf) = kD(f)”
Page 460, Change the first line below Formula (5) to read
“We leave it as an exercise to show that in the special case where is multiplication by C, and …”
Page 460, Change Formula (6) to read

Page 470, Change the beginning of Theorem 8.5.3 to read
“Two nn matrices, A and B, are similar if and only if there exist two bases for Rn (one for A and one for B) relative to which those matrices represent the same linear operator. Moreover…”
Page 486, Directions for Exercises 12-13
Change “an” to “the”
Page 495, instructions for Exercises 9-10
Change the last sentence to read: “Use Fomulas (9) and (10) to approximate the dominant…”.
Page 501, instructions for Exercises 3-4
Delete the word “in” at the start of the second line
Page 511, second displayed formula
The matrix to the right of the equal sign should read:
Pages 556 and 557 of ELA+Apps, Tables 1 and 2
In the table heading with the diagonal line, the letter “x” should be set in boldface, roman type (denoting a vector); the superscript is ok
Page 565 of ELA+Apps, first matrix on the page
The 3rd letter in the blue label at the top should be “D” and not “F”
Page 654 of ELA+Apps
In the Prerequisites box change “Linear Transformations” to “Matrix Transformations”
Where two page numbers are given below, the first applies to ELA and the second to ELA+Apps.
Page 531/723, Exercise Set 1.4, #21
Delete the part letter (b) and the associated answer, but leave the part letters and answers unchanged
Page 535/727, Exercise Set 2.1, True/False
Delete answer (f) and re-letter subsequent solutions as (f)-(i)
Page 535/727, Exercise Set 2.3, True/False answers
(l) should read: “False”
Page 536/728, Exercise Set 3.1, #11(a)
Delete the “u =”, and change the answer to read, “P(–1, 2, –4) is one possible answer.”
Page 536/728, Exercise Set 3.1, #11(b)
Delete the “u =”, and change the answer to read, “P(7, –2, –6) is one possible answer.”
Page 539/731, Exercise Set 4.3, True/False (a)
Should read: “False”
Page 551/743, Exercise Set 7.2, True/False
Part (f) should read “True”
Page 567/771 Index
Below the index entry for “Symmetric Matrices” change the page number for the subentry “orthogonally diagonalizing” from “299” to “399”

The following is a correction for the Student Solutions Manual

Page 19, Exercise Set 1.4, Exercise 21
Delete the solution to part (b), but leave the part labels and answers to (a), (c), (d), and (f) unchanged.

The following is a correction for the Instructor Solutions Manual

Page 20, Exercise Set 1.4, Exercise 20
Delete the solution to part (b), but leave the part labels and answers to (a), (c), (d), and (f) unchanged.

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