Question: In each case, (i) find a basis or ker T, and (ii) find a basis of m T. (a) T: P2 R2; T(a + bx

In each case, (i) find a basis or ker T, and (ii) find a basis of m T.
(a) T: P2 †’ R2; T(a + bx + cx2) = (a, b)
(b) T: P2 †’ R2; T(p(x)) = (p(0), p(1))
(c) T: R3 †’ R3; T(x, y, z) = (x + y, x + y, 0)
(d) T: R3 †’ R4; T(x, y, z) = (x, x, y, y)

(g) T: Pn †’ R; T(r0 + r1x + €¢€¢€¢ + rnxn) = rn
(h) T: Rn †’ R; T(r1, r2,..., rn) = r1 + r2 + +ˆ™ ˆ™ ˆ™ ˆ™+ rn

a+b b+c e+d d+u

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b Here T P 2 R 2 given by Tpx p0 p1 Hence ker T px p0 p1 0 If px a bx cx 2 is in ker T then 0 p0 a a... View full answer

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