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JakerGamer
14.02.2020 •
Mathematics
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
leftbracket3.gif 1 0 0 1
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0 0 1 0
0 0 0 0
(x1, x2, x3, x4) =
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Ответ:
The solution of the system is { (-t. s. 0, t) : s,t ∈ R}
Step-by-step explanation:
Lets multiply the first row by (x1,x2,x3,x4) and equalize to 0
(1,0,0,1) * (x1,x2,x3,x4) = x1+x4
which is equal to 0 only when
x1+x4 = 0
x1 = -x4
Now we can replace x1 with -x4.
If we multiply the second row (0,0,1,0) with (x1,x2,x3,x4) we will obtain (0,0,1,0)*(x1,x2,x3,x4) = x3. Since we want that product to be equal to 0, then x3 = 0. If we multiply the third row of zeros with (x1,x2,x3,x4) we will obtain automatically 0.
As a consecuence, we have 2 conditions:
x3 must be equal to 0x1 must be equal to -x4We call t = x4, s = x2, which can take any value. The solutions of the system is
{ (-t. s. 0, t) : s,t ∈ R}
Ответ:
s,
Step-by-step explanation: