This question concerns the following two subsets of R4.noitulos won ni S = {(0,1,3,2), (1,0, 1,0), (1,-1,-1,-1)}, ១រ.ខ... ed T= {(a, b, a+b+c, c): a, b, c = R}. stoodTa'quaralelques cl) elm bus ansool? (a) Show that SCT, and write down a vector in R4 that does not belong 99 99 to T. GRAND oy nadw and all (200 (b) Show that T is a subspace of R4 d FOR lantam 101) medaus Ja by sond Todu odr (c) Show that S is a basis for T, and state the dimension of T. cut saut to tavoms 943 Sabm UCT & DOY Gvin (d) Show that two of the vectors in S are orthogonal. Without using the mo Gram-Schmidt orthogonalisation, find an orthogonal basis for T.
This question concerns the following two subsets of R4.noitulos won ni S = {(0,1,3,2), (1,0, 1,0), (1,-1,-1,-1)}, ១រ.ខ... ed T= {(a, b, a+b+c, c): a, b, c = R}. stoodTa'quaralelques cl) elm bus ansool? (a) Show that SCT, and write down a vector in R4 that does not belong 99 99 to T. GRAND oy nadw and all (200 (b) Show that T is a subspace of R4 d FOR lantam 101) medaus Ja by sond Todu odr (c) Show that S is a basis for T, and state the dimension of T. cut saut to tavoms 943 Sabm UCT & DOY Gvin (d) Show that two of the vectors in S are orthogonal. Without using the mo Gram-Schmidt orthogonalisation, find an orthogonal basis for T.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
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Transcribed Image Text:noitulos wo
mi
This question concerns the following two subsets of R4:
S = {(0,1,3,2), (1,0, 1, 0), (1,-1,-1,-1)},
four baus ein
T = {(a, b, a+b+c, c): a, b, c ER}.
yo restoodTebquargal elques 161) esin
ein bos essoal?
(a) Show that SCT, and write down a vector in R4 that does not belong
to T.
frus
slunem 101) edmun
Jan Boy Tod
(b) Show that T is a subspace of R4.
mudun edr
(c) Show that S is a basis for T, and state the dimension of T.
dead sout to amuoms sis to moite
acper band-tigh
y
(d) Show that two of the vectors in S are orthogonal. Without using
Gram-Schmidt orthogonalisation, find an orthogonal basis for T.
mi sie od hirede show
inanonob as el vie
(e) Find an expression for the vector (3, 1,-1,-5) in T as a linearada yd
combination of the vectors in your orthogonal basis for T. blods noY
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