SOLUTION: Let A={ (1,2,k) , (-1,2k,1) , (k,-2,1) } . Find all the values for k , if any , such that (i)rank A = 1 (ii)rank A = 2 (iii)rank A = 3 .

SOLUTION: Let A={ (1,2,k) , (-1,2k,1) , (k,-2,1) } . Find all the values for k , if any , such that (i)rank A = 1 (ii)rank A = 2 (iii)rank A = 3 .

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Question 438728: Let A={ (1,2,k) , (-1,2k,1) , (k,-2,1) } . Find all the values for k , if any , such that (i)rank A = 1 (ii)rank A = 2 (iii)rank A = 3 .
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

~, R1 + R2
~, R2 <--> R3
~, -kR1 + R2
~, R2 + R3
For Rank 3: , -1
For rank 2: k = 2
For rank 1: k = -1.
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