4. (5 points) show that the set h = (1.x - 4y = z). ly: "}is a subspace of r3. state any theorems that you x + y = 0 use. p1 5. let t: p2 → r2 be the linear transformation defined by t (p) = |2o: (2) a) (2 points) calculate t(p), where (t) = t2 – 3t+7. b) (6 points) find a polynomial q which spans the kernel of t.

hi,

6x times 4 is 24x and 5 times 4 is 20, so the answer is 24x+20.

hope this and for a little humor i am groot.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4