Define-a-3-3-matrix-whose-entries-are-the-first-9-positive-integers-Let-s-k-be-the-sum-of-the-elements-across-the-kth-row-Is-there-such-a-matrix-where-s-1-s-2-s-3-1-2-3- Tinku Tara June 3, 2023 Algebra 0 Comments FacebookTweetPin Question Number 8236 by Yozzias last updated on 03/Oct/16 Definea3×3matrixwhoseentriesarethefirst9positiveintegers.Letskbethesumoftheelementsacrossthekthrow.Istheresuchamatrixwheres1:s2:s3=1:2:3?−−−−−−−−−−−−−−−−−−−−Whataboutn×nmatriceswhoseelementsarethefirstn2positiveintegers?Isthereamatrixsuchthats1:s2:s3:s4:…..:sn=1:2:3:…:n? Commented by Rasheed Soomro last updated on 03/Oct/16 s1+s2+s3=9×(9+1)2=45[∵s1∪s2∪s3={1,2,3,…,9}]If45isdividedin1:2:3s1=456=152.Butsumofthreewholenumbersmaynotbefraction.Sosuch3×3matrixisnotpossible.Similarilyforn×nmatrixs1+s2+s3+…+sn=n2(n2+1)2[∵s1∪s2∪s3…∪sn={1,2,3,…,n2}Ifs1:s2:s3:s4:…..:sn=1:2:3:…:ns1=n2(n2+1)2n(n+1)2mustbewholenumber.s1=n2(n2+1)2×2n(n+1)=n(n2+1)n+1Butthisisnotwholenumberingeneal.Soingeneralsuchn×nmatrixisnotpossible. Commented by Yozzias last updated on 03/Oct/16 Thanks! Answered by Yozzias last updated on 04/Oct/16 Answerincomments. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Every-day-for-n-days-you-put-either-1-2-or-3-into-a-saving-account-It-is-random-as-to-how-much-you-save-each-day-What-is-the-average-amount-you-will-have-saved-in-n-days-Next Next post: Question-73775 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.