document.write( "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 . \n" ); document.write( "

Algebra.Com's Answer #303322 by robertb(5830) $\"\"$ $\"About$

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$\"A+=+%28matrix%283%2C3%2C+1%2C2%2Ck%2C-1%2C2k%2C1%2Ck%2C-2%2C1%29%29\"$
\n" ); document.write( "~ $\"%28matrix%283%2C3%2C+1%2C2%2Ck%2C0%2C2k%2B2%2Ck%2B1%2Ck%2C-2%2C1%29%29\"$ , R1 + R2
\n" ); document.write( "~ $\"%28matrix%283%2C3%2C+1%2C2%2Ck%2Ck%2C-2%2C1%2C0%2C2k%2B2%2Ck%2B1%29%29\"$ , R2 <--> R3\r
\n" ); document.write( "\n" ); document.write( "~

, -kR1 + R2\r
\n" ); document.write( "\n" ); document.write( "~

, R2 + R3\r
\n" ); document.write( "\n" ); document.write( "For Rank 3: $\"k%3C%3E2\"$ , -1
\n" ); document.write( "For rank 2: k = 2
\n" ); document.write( "For rank 1: k = -1. \n" ); document.write( "

\n" );