# Student Solutions Manual for Elementary Linear Algebra with by Howard Anton, Chris Rorres By Howard Anton, Chris Rorres

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This vintage therapy of linear algebra provides the basics within the clearest real way, analyzing simple rules via computational examples and geometrical interpretation. It proceeds from widely used suggestions to the strange, from the concrete to the summary. Readers regularly compliment this impressive textual content for its expository sort and readability of presentation.

* The functions model encompasses a wide array of fascinating, modern applications.

* transparent, obtainable, step by step reasons make the fabric crystal clear.

* tested the difficult thread of relationships among structures of equations, matrices, determinants, vectors, linear adjustments and eigenvalues.

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Extra resources for Student Solutions Manual for Elementary Linear Algebra with Applications (9th Edition)

Sample text

3 4  x+ y 5 5  4 3 − x + y  5 5  Add –4/3 times Row 2 to Row 1. 1 0 1 51 52 Supplementary Exercises 1 Thus, x′ = 3 4 –x + – y 5 5 4 3 y′ = – – x + – y 5 5 3. We denote the system of equations by a11x1 + a12x2 + a13x3 + a14x4 = 0 a21x1 + a22x2 + a23x3 + a24x4 = 0 If we substitute both sets of values for x1, x2, x3, and x4 into the ﬁrst equation, we obtain a11 – a12 + a13 + 2a14 = 0 2a11 + 3a13 – 2a14 = 0 where a11, a12, a13, and a14 are variables. If we substitute both sets of values for x1, x2, x3, and x4 into the second equation, we obtain a21 – a22 + a23 + 2a24 = 0 2a21 + 3a23 – a24 = 0 where a21, a22, a23, and a24 are again variables.

0 11 10 1 7 10  1  0  0  3 2 −1 1 − 2 1 −3 −2 − Interchange Rows 1 and 2. 0 0 1     Add –3 times Row 1 to Row 2 and –2 times Row 1 to 3.     Add –1 times Row 2 to Row 3. 5 7. 33 (c) 1  0  1 0 1 1 1 1 0 1  0  0 0 1 1 1 1 −1 0 1 1 1 0 1 0 0 1 0 1 0  1  0   0   1   0   1  1 0 0 0 1 0 1 0 −1 0 0 1 0 1 0 1 0 1 2 0 1 1 2 1 2 1 − 2 1 2 −      0 0 1      0 0 1 − 2 1 2 1 2 1 2 Subtract Row 1 from Row 3.         1 2 1 2 1 − 2 Subtract Row 2 from Row 3 and multiply Row 3 by –1/2.

4 guarantees that A is invertible. 8 (b), Ak is also invertible. 4 allows us to conclude that Akx = 0 has only the trivial solution. 25. Suppose that x1 is a ﬁxed matrix which satisﬁes the equation Ax1 = b. Further, let x be any matrix whatsoever which satisﬁes the equation Ax = b. We must then show that there is a matrix x0 which satisﬁes both of the equations x = x1 + x0 and Ax0 = 0. Clearly, the ﬁrst equation implies that x0 = x – x1 This candidate for x0 will satisfy the second equation because Ax0 = A(x – x1) = Ax – Ax1 = b – b = 0 We must also show that if both Ax1 = b and Ax0 = 0, then A(x1 + x0) = b.