Question

1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent.

If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

(1 point) 13--3-3 Let vi = and V4 1-11 Linearly Dependent 1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent. If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter O's for the coefficients, since that relationship always holds. 11V + 18! V2+ III V4 = 0.

Answer 1

0 a 1-3 7 1-97 I U2= -2 7 ono 3 - L-31 [- a [ 44 We take the equation, 99 +64 +63 Uz tea q=0. » -34 -9 6 -42 Cz + 3 e4 20 .- o G -2 -2 ₂ + 2004 20 - ③ 1. G + 3 2 +18 e3 +0.6470 - © -39 -11 - 440 +5e4 zo 6 » [-3 -9 -42 37 ras 0 -2 -2 2 1 ن ndon - 1-3 -1 -44 S ICAK oo m P Now, to solve @ Pezo, we need to get the Echelon form of P. Scanned with CamScanner

Po RNR3 T 3 18 or Ti 3 18.07 1-3 | -11 -44 5 |R32RLER! 79 S P -3 -11 -44 5 1-3 -9 -423 10-2-22 To-2 - 22 o 10-2-22 Į Rfa R3-R4 í 3 18 or 3 18 07 Réz 3R + R2-3 105 -11 To -2 -44 To -2 10 +1 +1 -11 lo o ool 10:0 ondol 2.2 | Ry' 2 223 the 3 18 07 To -2 10 5 1 € - 0 ||2| 3 | oo oo In the Echelon from 'É of 'p' the pirof variables are leoxed first second and third column has pirst verables - Scanned with CamScanner

.. pezo ² Ec=0 1 3 18 oy rat 10 -2 105 To o 12 3 Loo oo 4, C2, C3, By are first variables and ca in free rariable. det, C42 t. ... 12 ez + 3 64 20 37463 +420 7 6 2 - 4 - and -2G +10 ez+S4 => 24₂ 2103 +54 210. + 5.6 2-t +stit » es ast and, a +34 +18 43 20 » 42 -34 -18 3 3-3. St +18. 1 2 -15t + 18t 3 2 - 15 X Scanned with CamScanner

I at I 5 ses) any scalar Now, since, the Echelon foom (E) of P has a zero row, so the matrix e has rank 3. - Hence, the system E has a with trivial solution. So, it can lee concluded that the reetors 4, U2, Uz and on are linearly dependent for any non zero t, we get a nou zero, non triral solution sit of a,cs, o and ci euch that GetG uz tG 43 +44 20 holds. det t= 4, them (9,2,3,4)=(3,5,-1,4) on :. 34 +5 U2 -Uz +40 20 Scanned with CamScanner