Question: Null space (linear combination)

Suppose that S={u1,u2,u3,u4,u5,u6}⊂ℝ5  where

u1=  < -17, -29, 6, -81, 20>

u2 = <-65, -11, -47, 18, -15>

u3 = <-240, 90, -265, 495, -175:>

u4= <-53, 70, 84, -80, 61>

u5= <9, 0, 46, -55, -37>

u6 =< 176, -280, -520, 540, -96>

Find a possible set of values for λ1, λ2, λ3, λ4, λ5, λ6, not all zero, such that  

 

λ1u1+λ2u2+λ3u3+λ4u4+λ5u5+λ6u6=0 .

 

Enter the values of  λ1, λ2, λ3, λ4, λ5, λ6  as a sequence in the box below

 

[λ1, λ2, λ3, λ4, λ5, λ6]= 

 

Hint: There are infinitely many solutions for λ1, λ2, λ3, λ4, λ5, λ6 .   The solution given by Maple will be in terms of parameters. To get one possible set of values, not all zero, choose some nice values for the parameters.

 

CAN ANYONE HELP ME WITH THIS QUESTION. I DO NOT KNOW HOW TO APPROACH THIS QUESTION. CAN I GET A SETP BY STEP SOLUTION PLS. THANKS.

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