Question

Linear Algebra (Vectors) - Practice Problem

Please only answer if you are 100% sure of solution. Thank you.

(1 point) Determine which of the following sets of vectors are linearly independent and which are linearly dependent. 2 2 1. 4 ✓ Select an answer Linearly independent Linearly dependent -9 B 23 1 -17 14 Select an answer 2. 11 23 -46 Select an answer 3. -3 -4 -27 -36 -8 -10 -5 3 10 -5 1 3 -10 -5 Select an answer 4. -9 -4 -4 -7 -7 4 -9 -4 6 6 3 -1 5 Select an answer 5. 18 -7 -7 -7 3 4 5 10 -2 -4 Select an answer 46. 3 6 4 8

Answer 1

we willl check by Matrix Memod :- 5 4 - 2 2 R2 R2+2 R1 -2 5 1 [ N ] nou-rero linearly Independent Both Rows ane 5 -5 -4 -4 - 1 14 17 11 23 5 R2-RI R2 R3 → R3 +17Rz -3 5 ** -5 -15 o -22 -6 -45 O -54 54 R2 R3 B 22 RB -3 -5 -15 -2 -22 ooo -24 - 180 0 R3 R3-12R2 -3 - 5 S -15 0 -22 6 O Unearly Dependent zero is One Row -4 -5 6 9 -7 10 33 46 -27 -36 10 R3+ 46 R2 R37 linealy Independent Re R2+2R nou reno 4 ave All Rows --5 DOG too 8 0

(4 8 -5 -9 it lo -4 3 -5 3 -4 -7 6 6 clo 10 - 5 -7 Re AR2-5R1 R5 R8tR R3+2R3 - R2 Ry 5Ry +3 R3 -8 5. -9 ใ -9 29 29 21 7 its process, see As you cam very long has Basis 4. rele IRA Perore see ces you vectors is linearly more of than 4 sel- consists any dependent This is time arly dependent of IRA 5 rectors because contains is