MA 35100 Lecture Notes - Lecture 26: Xfl, Linear Map, Indep
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Multiply by inverse - assumes an inverse exists: -> r, + ry. 0 0-3-2-1 - i po o -1 afals. Ry -> re -2r, word) on 26 afo if c. Section 3. 5: the matrix of a linear transformation coordinates. Recall: think of a basis (informally) for a vs. as a set of coordinate axes. Soit xct, we can write it as x=cx,+[nxr. If b is linearly indep. choice of scalars is unique. If c. x1 + . (nxn = dx1+dnxm so (cidi)x,+(cn-dn) xn = 8. Since [x,xn3 is linearly indep, all ci-di = 0. If x = cx1+ . cmxn we call [c] -r" the rector of coordinates. Now take 75: 3(2), (373, also basis for r. =in py, we have the standard basis 73:51,x, x3, x33 aethe and 5:31+x,2xcx+x7, x33 is also a basis for p3. The cubic with ecoora-vector (3) is 2+4x+3x"-x3 < has b cord rector:
