Find the standard matrix for the following transformation t : r4 → r3: t(x1,x2,x3,x4) = (x1 −x2 +x3 −3x4,x1 −x2 +2x3 +4x4,2x1 −2x2 +
x3 +5x4)
(a) compute t(e⃗ ), t(e⃗ ), t(e⃗ ), and t(e⃗ ).
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(b) find an equation in vector form for the set of vectors ⃗x ∈ r4 such
that t (⃗x) = (−1, −4, 1). (c) what is the range of t?