{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math103hw4solns

# math103hw4solns - Note Title 13 Here 55‘ is not in V as...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Note Title 13. Here, 55‘ is not in V, as We ﬁnd an inconsistency while attempting to solve the system. 30. Let’s build B “oolumn-hy-eohuml”: B = [[TWL)]B[TW2)]BETW\$}]5] [H0 2 i W H0 2' 4] W H0 2 4] Hi i = 2 —1 0 1 2 —1 D 1 2 —1 0 .2 4 -4 1 1'- 3 4 —4 1 2 B 4 —4 l 4 3 [H H [OH [1”] ' = 1 —l 0 = 0 H]. U . 1 B —2 B s B '. 0 o e 38. We went a basis 5 = (171,232) such that TEE} = as, and TE?) = be; for some scalars a and h. Then the B—matrix of T will he B = [[T{ﬂ'1}]g [Tfﬁzjlg] = [3 g], which 11? for vectors parallel to the —u'5' = (—lJ-u'i for vectors perpendicular to L. lei to L and 6'2 is perpendicular, for example, is a diagonal matrix as required. Note that TIE‘U} = r? = Line L about which we reﬂect, and Tftm 2 Thus, We can pick a. basis where 6', is para] editiﬁi) HEN; *i:5i=i§i' I—IJ—t a? E 5-” Q 5* + S1 + £1. + 51 I'i 6- The} = Ti-ﬁo — 61 — 63) = 4%) — T071) — Tfﬁg) =—e—e—e=e Hence, T is a. rotati 9 ' " given by on through 120 about the hne spanned by eg. Its matrix, B, is [[TiﬁiisiTiﬁ‘aiis [Thishsi where —I Tfﬂi)=5’o = at; 452—5330 [21171)]3: [-1] —1 0 Tirhj=ﬁgsoITW2JIs= 1 U 1 T(?Ta)_=17*1 50 [T(53}IH= U U —1 D 1 andB= —l 1 0 . l 0 0 33 = Ia since if the tetrahedron rotates through 120° three times, it returns to the original position. 73. e = 5-1113, where s = A = [:33 "233] Thus B = A = [2:38; ‘28] - ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online