By Howard Anton, Chris Rorres
Easy Linear Algebra eleventh version provides an common therapy of linear algebra that's appropriate for a primary direction for undergraduate scholars. the purpose is to give the basics of linear algebra within the clearest real way; pedagogy is the most attention. Calculus isn't really a prerequisite, yet there are truly categorized routines and examples (which will be passed over with no lack of continuity) for college kids who've studied calculus.
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Extra resources for Elementary Linear Algebra: Applications Version (11th Edition)
Sample text
AB = A[b1 b2 · · · bn ] = [Ab1 Ab2 · · · Abn ] (6) (AB computed column by column) ⎡ ⎤ a1 ⎢a ⎥ ⎢ 2⎥ ⎡ ⎤ a1 B ⎢a B ⎥ ⎢ 2 ⎥ AB = ⎢ . ⎥B = ⎢ . ⎥ ⎣ .. ⎦ ⎣ .. ⎦ am am B (7) (AB computed row by row) We now have three methods for computing a product of two matrices, entry by entry using Definition 5, column by column using Formula (8), and row by row using Formula (9). We will call these the entry method , the row method , and the column method , respectively. In words, these formulas state that j th column vector of AB = A[ j th column vector of B] (8) i th row vector of AB = [i th row vector of A]B (9) E X A M P L E 7 Example 5 Revisited If A and B are the matrices in Example 5, then from (8) the second column vector of AB can be obtained by the computation ⎡ 1 2 2 6 ⎤ 1 4 ⎢ ⎥ ⎣−1⎦ 0 7 27 −4 ✛ ✛ Second column of B = Second column of AB 32 Chapter 1 Systems of Linear Equations and Matrices and from (9) the first row vector of AB can be obtained by the computation ⎡ [1 2 4 ⎢ 4 ]⎣0 2 1 1 7 4 3 5 ⎤ 3 ⎥ 1⎦ = 2 [ 12 27 30 13 ] First row of A Matrix Products as Linear Combinations Definition 6 is applicable, in particular, to row and column vectors.
Am am B (7) (AB computed row by row) We now have three methods for computing a product of two matrices, entry by entry using Definition 5, column by column using Formula (8), and row by row using Formula (9). We will call these the entry method , the row method , and the column method , respectively. In words, these formulas state that j th column vector of AB = A[ j th column vector of B] (8) i th row vector of AB = [i th row vector of A]B (9) E X A M P L E 7 Example 5 Revisited If A and B are the matrices in Example 5, then from (8) the second column vector of AB can be obtained by the computation ⎡ 1 2 2 6 ⎤ 1 4 ⎢ ⎥ ⎣−1⎦ 0 7 27 −4 ✛ ✛ Second column of B = Second column of AB 32 Chapter 1 Systems of Linear Equations and Matrices and from (9) the first row vector of AB can be obtained by the computation ⎡ [1 2 4 ⎢ 4 ]⎣0 2 1 1 7 4 3 5 ⎤ 3 ⎥ 1⎦ = 2 [ 12 27 30 13 ] First row of A Matrix Products as Linear Combinations Definition 6 is applicable, in particular, to row and column vectors.
19. 23 = 9 = 11 = 8 = 10 Z3 + Z4 −Z1 − Z2 + 2Z3 − 3Z4 Z1 + Z2 − 2Z3 2Z1 + 2Z2 − Z3 + Z5 + Z5 − Z5 + Z5 =0 =0 =0 =0 In each part of Exercises 23–24, the augmented matrix for a linear system is given in which the asterisk represents an unspecified real number. Determine whether the system is consistent, and if so whether the solution is unique. Answer “inconclusive” if there is not enough information to make a decision. In Exercises 9–12, solve the linear system by Gauss–Jordan elimination. 9. Exercise 5 10.