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errata

# errata - Appendix E Errata These errors have been...

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Appendix E - Errata These errors have been discovered since the second printing in 1996. There is a previous page of errors that were corrected in the second printing. Page 18, Exercise D4 The reference to D5 should be to D3. Page 21 The line after the first equation should read -→ AB = b a . Page 25 line 1, equivalent. Page 73, Example 6 left matrix, last row, last entry should be 2 (and not 2). Page 146 second line from the bottom should be g ( k x ) negationslash = kg ( x ). Page 185, B2(d) As defined, the set is empty (no x can satisfy the equation), so the set is not a subspace. This is not what was intended. Replace (1 , 1 , 1) on the right-hand side of the equation by (2 , 3 , 4); then the set is not empty, but it is not a subspace because is it not closed under the addition or multiplication by scalars. Page 207 The discussion of L is wrong. L is lower-triangular, but it does not have such a simple form. However, by examining carefully inverses and products of lower triangular elementary matrices (and the order is very important), we can show that L - 1 = 1 0 0 . . . 0 12 1 0 . . . 0 . . . . . . . . . . . . n 1 n 2 n 3 . . . 1 , where the ij are as described on page 206. Then, in the next paragraph, instead of “ LU = A ” we have LA = U so A = L - 1 U , and this is the claimed decomposition of A into the product of a lower triangular matrix L - 1 with an upper triangular matrix U . The solution procedure described in the middle of page 207 must be revised to agree with this, and in the matrix at the bottom of page 207, the below diagonal entries should be ij to agree with the notation on page 206. (In fact, it would be better to revise the notation on page 206 so that we do get A = LU ; such a revision is presented starting on page E-2.)

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