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}

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

for point B:

The set B is part of the subspace

for point C:

In this, the scalar multiplication can't behold

∉ C

this inequality is not hold

The set C is not a part of the subspace

for point D:

The scalar multiplication s is not to hold

∉ D

this is an inequality, which is not hold

The set D is not part of the subspace

For point E:

The   is the arbitrary, in which is arbitrary  

The set E is the part of the subspace

For point F:

The arbitrary so, they have as the arbitrary

The set F is the subspace of

7

step-by-step explanation:

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92