Please help me with this problem.
1 answer:
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Answer:
#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never
Step-by-step explanation:
#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1). First we simplify our equation using the distributive property:
y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6
Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4. Using point-slope form,
#2) We must first write our second equation in slope-intercept form by isolating the y term:
2x+y=7
Subtract 2x from each side"
2x+y-2x = 7-2x
y = -2x+7
This means the slope is -2; the slopes are the same, so the lines are parallel.
#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,
#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.
#5) Two lines with the same slope are always parallel. They are never perpendicular.
Answer:
E is not a subspace of
Step-by-step explanation:
E is not a subspace of
In order to see this, we must find two points (a,b), (c,d) in E such that (a,b) + (c,d) is not in E.
Consider
(a,b) = (1,1)
(c,d) = (-1,-1)
It is easy to see that both (a,b) and (c,d) are in E since 1*1>0 and (1-)*(-1)>0.
But (a,b) + (c,d) = (1-1, 1-1) = (0,0)
and (0,0) is not in E.
By the way, it can be proved that in any vector space all sub spaces must have the vector zero.