- #1
dmitriylm
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Homework Statement
1. Express the general solution of the following system in vector form.
2x + 4y + 6z + 4w = 4
2x + 5y + 7z + 6w = 3
2x + 3y + 5z + 2w = 5
Clearly identify the particular solution. Also produce a vector with no zero components that satisfies the corresponding homogeneous system.
Homework Equations
The Attempt at a Solution
The solved echelon form is:
2x + 4y + 6z + 4w = 4
0x + 1y + 1z + 2w = -1
x = 4 + 2w -z
y = -1 - z - 2w
solution set: (4-z+2w, -1-z-2w, z, w)
The solution in vector form is displayed as:x |0 | |4 | | -1 | | 2|
y = |0 |+ |-1|+ | -1 |z + | 2|w
z |0 | |0 | | 1 | | 0|
w |0 | |0 | | 0 | | 1|The particular solution is the vector:
|4 |
|-1|
|0 |
|0 |
What I'm confused by is this statement: "Also produce a vector with no zero components that satisfies the corresponding homogeneous system.". What is the corresponding homogeneous system? How do I find it? How do I then produce this vector with no zero components?
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