Errors in Elementary Linear Algebra

• 12th May 2015. Serban Raianu noticed the following typos in Chaper 7: row +7: x_1 and y_1 should be written in terms of x and y, not x_1 and y_1. Then later on row +11, the dash is missing from x_2-axis. These have been fixed.
• 7th May 2015. Robert Adams noticed the extra "as" in problem 10, page 87.
• 28th March 2015. Ashley Dorris noticed a missing x₅ in the answer to problem 6 of secction 3.6 on page 33.
• 3rd March 2015. Jacob Gharibian noticed that the (2,3) entry of the matrix on line 2 of problem 2, should be 1. The rest of the solution is correct.
• 2nd March 2015. Mark Warnholtz has pointed out a missing denominator 2 in the 1-2 entry of the square matrix at the end of the solution to problem 5, Section 2.4. This has now been fixed.
• 3rd December 2013. Boian Kolev has pointed out that on the first page of the Chapter Identifying Second Degree Equations, "We show that it is always possible to rotate the x, y axes to x_1, x_2 axes" should read "We show that it is always possible to rotate the x, y axes to x_1, y_1 axes." This has been fixed.
• 28th November 2013. The previous error has now been fixed.
• 26th November 2013. Laura Yamashiro has pointed out that in problem 4 (iv) of problem set 7.3, the centre of the hyperbola is (-1/10, -7/10).
• 5th November 2013. The previous two errors have now been fixed.
• 5th November 2013. Laura Yamashiro has pointed out that in the solution to Problem 9, Section 4.1, in the reduced form of B, the (1,3) element should be 2/3, not -2/3. Then the solution for x is x=-2/3+2z/3. This has not yet been fixed.
• 3rd November 2013. Boian Kolev has pointed out that in the solution to Problem 2 of section 4.1, there should be a + sign between the last two determinants on the last line of page 43. This has not yet been fixed.
• 27th April 2013. Joseph Sheue noted two errors in Example 7.1.4, page 140. In the equation following the line "The original quadratic equation becomes", replace the √5 on the numerator by 5. Two lines further on, replace √5(y₁ - 2√5) by -√5(y₁ - 2√5). This has now been fixed.
• 24th April 2013. Serban Raianu pointed out that equation (7.16) contained an extra + sign. This has now been fixed.
• 17th April 2013. Serban Raianu pointed out that on page 123 on lines 5 and 7, 3^n-1 should be replaced by 3ⁿ. This has now been fixed.
• 16th April 2013. Serban Raianu pointed out that on page 123 we have x_n=(2n+1-3ⁿ)/4, not x_n=(2n-1+3ⁿ)/4. This has now been fixed.
• 26th March 2013. Joseph Sheue pointed out that in sol4.pdf, the solution to problem 7(c), page 34, last line had $R(A)$ instead of $N(A)$. This has now been corrected.
• 16th February 2012. Vladimir M. of St. Petersburg pointed out today that on page 29, the (1,2) entry of A(BC) should be sin ψ sin φ cos θ. This has now been fixed.
• 13th February 2012. Vladimir M. of St. Petersburg pointed out on 12th February that on page 29, all occurences of sin ψ should be replaced by -sin ψ. This has now been fixed.
• 10th February 2010. Fixed the previous errors including the typo "contradictiong" in Chapter 3. Also did some formatting.
• 26th March 2007. Skip Thompson pointed out that I had not defined d on page 145. In fact d = 2a(gh - af). I then noticed that k should be (ag + hf)/(a + b), not (ag + bf)/(a + b).
• 4th April 2007. Gabor Sebo pointed out a typo (around old page 93) in the solution to Example 5.2.1: y=1/(2x) not b/(2x). He also suggested a slight improvement to the exposition of the first example in section 5.2, which I subsequently implemented.
• 16th May 2006. Jeff Post observed that in the solution manual, page 88, problem 6, "Let A = (3,5,6)" should be "Let A = (-3,5,6)". And on page 96, a little more than halfway down, "See figure below.)" should be either "(See figure above.)". Fixed.
• 3rd May 2006. Jeff Post pointed out that on the last line of page 159 "-||x|| ||y is proved similarly." should be "-||x|| ||y|| is proved similarly." Fixed on 16th May 2006.
• 1st May 2006. Fixed the following errors pointed out by Jeff Post:
  Solution manual page 74, problem 9(a):

  On the second line, for the det(λ I₃ - A), the (2,1) entry should have been -1/4, not 1/4. The minus sign was also missing from the last determinant on the third line, in position row 1, column 1:

  -1/4		-1/2
  -1/4		λ - 1/2

• 27th April 2006. Fixed the following errors pointed out by Jeff Post:
  (a) Page 135, Remark 7.1.2, second line contained a repetition "these these vectors".
  (b) Page 126, Problem 6, part (b): in the matrix, the minus sign was on the wrong 'b'.
  (c) Page 123, four lines above Theorem 6.2.2. Deleted the 'a' in "The discussion is a more ..".
• 4th April 2006. Fixed errors on page 36 and 77 of book and on page 40 of solutions.
• 4th April 2006. Jeff Post noted the following error: On page 77, just before Theorem 4.0.7, "Theorem 3.0.2" should be "Theorem 4.0.3". Not yet fixed.
• 23rd March 2006. Jeff Post noted the following typos:
  (a) Page 36, Question 8, "use Question 6" should be "use Question 7". Similarly for Question 10.
  (b) Solutions, page 40, problem 18, "u ∈ R & v ∉ S" should be "u ∈ R & u ∉ S". Not yet fixed.
• 17th December 2005. Some figures were missing from the pdf version of the complete book. These have been restored. Also the index has been out of alignment for some time and this has now been fixed.
• 3rd June 2005. I fixed the preceding error.
• 22nd April 2005. Craig Bauer has pointed out that I used x₂ instead of y₁ in the application of Theorem 6.2.1 to solving a system of linear differential equations on page 121. This will be corrected in the near future.
• 10th December 2004. I realized that in the recent update, I had absent-mindedly forgotten to include eps figures in chapters 5 and 8. This has now been corrected.
• 11th November 2004. Michael Osborne pointed out a typo on page 176: (a₂,b₂,c12 should read (a₂,b₂,c₂).
• 20th October 2002. Christoph Mitterer pointed out that on page 95, line 5, namely i should read namely 1.
  
• 5th July 2002. Christoph Mitterer pointed out that on page 62, Remark 3.4.1, would be linearly independent should read would be linearly dependent.
  Also (with Prof. Manfred Gruber) on page 126, Problem 6, labelling the elements of the matrix A with letters a,b,c,d was pointed out as being potentially confusing to the student reader. I changed this to a₁₁,a₁₂,a₂₁,a₂₂ on 11th November 2004.
• 4th July 2002. Christoph Mitterer pointed out a misprint on page 56, Example 3.2.3, where I had E_m, instead of E_n.
• 26th October 2001. William Romaine pointed out that in Example 1.4.7, page 15, the second equation should read 2x+2y+z=0.
• 7th November 2001. William Romaine observed that on page 15 of the solution to problem 9 of Problems 2.4, the polynomial x²-x+1 should be x²-x-1.
  Consequently on line -6, the formula for Aⁿ should read

  Aⁿ=k_nA+k_n-1I₂,

  with three flow-on errors on lines -3 and -4.