Linear combination and linear independence, Lecture notes of Linear Algebra

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Linear Combination and Linear Independence Note Title 24-02-2021 The expression cyvy + vo +++: + cy, is called a linear combination of vectors V1, V2,...,Vk © IR", where cy, co,..., Cc are scalars. A set of vectors {v1,V2,...,Vv«}is said to be linearly independent if the only scalars C1, C2,..., Ck satisfying cyvy + CoV2 +--- + cv, = 0 are cy = GQ = a fep 0. If vectors are not linearly independent, they are linearly dependent. J Examples @ Express the vector b = | as a linear combination of the vectors wf AK=% | LI -- soln. b= OH +Gh+e%, GratGer 2 \ \ \ 5G +2 thQ=i3 =G a\ra[e\s[4 (3) 7 3 © -a4G +3426 1 \ 1 Lv tot 1 z M= |5 2 4 | = | ~ 5 ok °| aA 1.3 6 o 2 4 let Rg > Rt ~ \ ov ve - o 14 \3 R >e&-5% oni => o 2 h\& ener? yr?” Qos we Vex ~ tA W\g L we, % 6 % eo Ry > Pathe Rankiiy= Ronk CAlb> = he of yorigels — unique aon O+G+QG=ad -3G6-QG@ =3 BQ=\0 > G- 3, Gr-2, Gea) Ver’ 48 Gokk BBE)