Consider the system of equations x−y−z=1 −x + 2y +4z = 2 x + 2y + 8z = c For what value(s) of c does the system have no solutions, a unique solution, infinitely many solutions? Give the solutions explicitly, when they exist. Answer: Inconsistent, if c ≠ 10. If c = 10, infinitely many solutions given by [x y z] = t [ -2 -3 1] +[ 4 3 0] where t is any scalar. if c = 10 the three planes intersect in a line whose parametric equations given by the solution vectors
Consider the system of equations x−y−z=1 −x + 2y +4z = 2 x + 2y + 8z = c For what value(s) of c does the system have no solutions, a unique solution, infinitely many solutions? Give the solutions explicitly, when they exist. Answer: Inconsistent, if c ≠ 10. If c = 10, infinitely many solutions given by [x y z] = t [ -2 -3 1] +[ 4 3 0] where t is any scalar. if c = 10 the three planes intersect in a line whose parametric equations given by the solution vectors
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I really need help with it because this has to be done in the matrix way, can you show steps and make the steps clear enough for me to understand.
It has to be done in the matrix form
Consider the system of equations
x−y−z=1
−x + 2y +4z = 2
x + 2y + 8z = c
For what value(s) of c does the system have no solutions, a unique solution, infinitely many solutions? Give the solutions explicitly, when they exist.
Answer: Inconsistent, if c ≠ 10. If c = 10, infinitely many solutions given by [x y z] = t [ -2 -3 1] +[ 4 3 0] where t is any scalar. if c = 10 the three planes intersect in a line whose parametric equations given by the solution vectors
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