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normahernandez977
20.09.2020 •
Mathematics
Which of the following sets are subspaces of R3 ?
A. {(x,y,z)|3x+8y-5z=2}
B. {(x,y,z)|-4x-9y+7z=0}
C. {(x,y,z)|x
D. {(-4,y,z)|y,z arbitrary numbers}
E. {(x,0,0)|x arbitrary number}
F. {(-2x,-3x,-8x)|x arbitrary number}
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Ответ:
The following are the solution to the given points:
Step-by-step explanation:
for point A:
The set A is not part of the subspace![R^3](/tpl/images/0771/0226/8ce53.png)
for point B:
The set B is part of the subspace![R^3](/tpl/images/0771/0226/8ce53.png)
for point C:![\to C={(x,y,z)|x](/tpl/images/0771/0226/e1f4c.png)
In this, the scalar multiplication can't behold
this inequality is not hold
The set C is not a part of the subspace![R^3](/tpl/images/0771/0226/8ce53.png)
for point D:
The scalar multiplication s is not to hold
this is an inequality, which is not hold
The set D is not part of the subspace![R^3](/tpl/images/0771/0226/8ce53.png)
For point E:
The
is the arbitrary, in which
is arbitrary
The set E is the part of the subspace![R^3](/tpl/images/0771/0226/8ce53.png)
For point F:
The
arbitrary so, they have
as the arbitrary ![\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F](/tpl/images/0771/0226/25f80.png)
The set F is the subspace of![R^3](/tpl/images/0771/0226/8ce53.png)
Ответ: