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 .

Algebra ->  Matrices-and-determiminant -> 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 .       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+%28matrix%283%2C3%2C+1%2C2%2Ck%2C-1%2C2k%2C1%2Ck%2C-2%2C1%29%29
~%28matrix%283%2C3%2C+1%2C2%2Ck%2C0%2C2k%2B2%2Ck%2B1%2Ck%2C-2%2C1%29%29, R1 + R2
~%28matrix%283%2C3%2C+1%2C2%2Ck%2Ck%2C-2%2C1%2C0%2C2k%2B2%2Ck%2B1%29%29, R2 <--> R3
~, -kR1 + R2
~, R2 + R3
For Rank 3: k%3C%3E2, -1
For rank 2: k = 2
For rank 1: k = -1.