Answer:
a) v ∈ ker(<em>L</em>) if only if ![[V]_{E}](https://tex.z-dn.net/?f=%5BV%5D_%7BE%7D)
∈ <em>N</em>(<em>A</em>)
b) w ∈ <em>L</em>(<em>v</em>) if and only if ![[W]_{F}](https://tex.z-dn.net/?f=%5BW%5D_%7BF%7D)
is in the column space of <em>A</em>
<em />
<em>See attached</em>
Step-by-step explanation:
See attached the proof Considering the vector spaces <em>V</em> and <em>W</em> with other bases <em>E</em> and <em>F</em> respectively.
Let <em>L</em> be the Linear transformation form <em>V</em> and <em>W</em> and A is the matrix representing <em>L</em> relative to<em> E</em> and <em>F</em>
So try to isolate a by division and such
K=4a+9ab
we use reverse dstributive which is ab+ac=a(b+c) so
undistribute a
4a+9ab=a(4+9b)
k=a(4+9b)
divide both sides by (4+9b)
=a
a=
So that equation was definitely correct...
When you expand the equation in the bracket you'll find out that you'll get a^6 + 4a^4 + !6a^2 - 4a^4 - 16a^2 -64. then your final result will be a^6 - 64
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<h3>Option A</h3><h3>3x - y = -5 is the equation of the line with a slope 3 and y intercept 5</h3>
<em><u>Solution:</u></em>
<em><u>The slope intercept form of equation is given as:</u></em>
y = mx + c ------ eqn 1
Where,
m is the slope of line
c is the y intercept
From given,
slope = m = 3
y intercept = c = 5
<em><u>Substitute m = 3 and c = 5 in eqn 1</u></em>
y = 3x + 5
3x - y = -5
Thus the equation of line is found
