MA 35100 Lecture Notes - Lecture 15: Triangular Matrix, Linear Combination
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: find a basis for a 3 3 upper triangular matrix . X , y e s ; + yes. C- s ; s es (cid:8869) linear combination remains in the set . Closed under linear (o es) combination . (cid:8869) yes . When 8=0 ez - _ [{ "%] es = [: = /eee) B = { ej } ? a ei + b ez + c ez + d ey + e. eg + fe a. [ee] e [ ] fab c: de ] = { { ] (cid:15482) a + b + ct ate + f = 0 in dep . Does this spans ? (span b = 8 ? : de] = a e , + b ez + c ez + de y te est feg > so. , and the aim (b) = 6 . " theorem 2. 8 : given a v. s . W with dim ( v) = n ,
