Differential Equations: An Introduction to Modern Methods and Applications

3rd Edition

ISBN: 9781118531778

Author: James R. Brannan, William E. Boyce

Publisher: WILEY

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Textbook Question

Chapter A.2, Problem 5P

In each of Problems 2 through 5, if there exist solutions of the homogeneous system of linear equations other than x = 0 , express the general solutions as a linear combination of linearly independent column vectors.

x 1 − 2 x 2 + x 4 = 0 2 x 1 + x 2 + x 3 − x 4 = 0 x 1 + 2 x 2 + x 3 − 2 x 4 = 0 3 x 1 + 3 x 2 + 2 x 3 − 3 x 4 = 0

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Chapter A.2, Problem 4P

Chapter A.2, Problem 6P

Students have asked these similar questions

Solve the following system of linear equations using linear combinations of column vectors. 2x + y + 12z = 1 -2x -4y -18z = 2

Solve each of the following systems of equations. Express the solution in vector form. (a) x+y+2z=4 2x + 3y +62 = 10 3x + 6y + 102 = 17 21 + 2x2 - 3x3 + 2xd = 2 2x1 +5x28x3 + 6x4 = 5 3x1 +4x25x3 + 2x4 = 4 x+2y+3z=3 2x+3y + 8z = 4 5x+8y + 192 = 11 1+3x2+2x3-24-25 = 0 2x1 + 6x2 + 5x3+4x4-25=0 5x1 + 15x2 + 12x3 +24-325 = 0 YYY (b) (c) (d)

2. Solve each of the following systems of linear equations by Gaussian elimination and back substitution. Write your answers as vectors or as linear combinations of vectors if appropriate. 2x + 2y + 2z = 2 -2.x1 + x2 + 5x3 b) -8x1 + 7x2 + 19x3 -10 a) 4х + 6у + 62 4 -42 6x + 6y + 10z 2

Chapter A Solutions

Differential Equations: An Introduction to Modern Methods and Applications

Ch. A.1 - Given the matrices...Ch. A.1 - If A=(120321213) and if B=(102011213), find...Ch. A.1 - Demonstrate that A=(223101111) and B=(112011102)...Ch. A.1 - Prove each of the following laws of matrix...Ch. A.1 - 5. If , under what conditions is to be...Ch. A.1 - 6. Prove that sums and products of upper(lower)...Ch. A.1 - Let A=diag(a11,.....ann) be a diagonal matrix....Ch. A.1 - Prove that if A is symmetric and nonsingular, then...Ch. A.1 - Two square matrices A and B are said to commute if...Ch. A.1 - 10. If is any square matrix, show each of the...

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Solve for X in the Equation, given A=-401-532 and B=12-2144 a 3X+2A=B b 2A5B=3X c X-3A+2B=0 d 6X4A-3B=0
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