Question

Question 4 [10 points) Consider the following vectors: a= For each of the following vectors, determine whether it is in span{a,b,c). If so, express it as a linear combination using a, b, and c as the names of the vectors above. V1 = <Select an answer > < Select an answer > Vy is not in span{a,b,c} V1 is in span{a,b,c} <Select an answer > anotomon V3 = <Select an answer >

Answer 1

* Sol Gimen - -3.- a- 6 b= 2 1-31 ( 3) let b2 = an+by+ cz 99+by+ c 2 =V, lo -31 - 02 + 24 + 42-18 Augmented matry ro -3 -5 67 1 3 L3/ L-5 -3 -5 107 w w NW Augmented matro lo 10 -3 -1 6 1 3 3 -4 Ri(-) Ry Fl 33-47 -5 ho -3 -5 6] R₂ +223 + 3 R2, Ry2Ryt32 li33-47 -Doo 2 و وا اله UL 3 3 Risory 3 3 -5 0 2 4 -8 10 -3 -1 2 To -3 -5 10 R₂ Q R 3 + 3 Re , Ry 7 2 R2, +3R2 1 3 3 -57 Tozu -8 loo 10-20 loo 2 -4) Ry 5Ry - Rz 13 3 -51 o 2 4 -8 / 10 o 10 -20 lo 0 0 0 1+34 +32 3-5 24 +43 = -6 102=-2D >2=-2 2y-8= f >y-0) 2+0-6=-5 - 12) H: V = (1)9,+(0) 6+(-2)C) :: V; ū a span { a, b,c} Rut Shy-R3 13 § -47 o24 -4 0 0 100 102=0 >>2=0 2y +42=-4 (4=-2] 1+34 +32=-4 1-62-4 :: V j a span {a,b,c} V₂ = (2) a + (-2) b + (0)

let antby +22=63 Augmented madre ro -3 lo 2 4 -3 -1 0 3 3 Rit Ry II 33 - lo 2 4 -9 10 -3 -5 -9) R3 2R3+3R2, Ry > 2R, +3R2 ci 3 3 -87 ..loa 4 -9 q Too 2 -45] Ry SR-R₃ si 3 3 -87 wloa 4 - 1 To o 10 -27 To oo -198] rank =4. .: Vg is not span {9,6,c}