{"id":577,"date":"2023-10-19T10:50:18","date_gmt":"2023-10-19T05:20:18","guid":{"rendered":"https:\/\/samacheer-kalvi.com\/?p=577"},"modified":"2023-11-10T10:36:54","modified_gmt":"2023-11-10T05:06:54","slug":"samacheer-kalvi-10th-maths-guide-chapter-3-ex-3-18","status":"publish","type":"post","link":"https:\/\/samacheer-kalvi.com\/samacheer-kalvi-10th-maths-guide-chapter-3-ex-3-18\/","title":{"rendered":"Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.18"},"content":{"rendered":"

Students can download Maths Chapter 3 Algebra Ex 3.18 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide<\/a> Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.18<\/h2>\n

Question 1.
\nFind the order of the product matrix AB if
\n\"Samacheer
\nAnswer:
\nGiven A = [aij<\/sub>]p\u00d7q<\/sub> and B = [aij<\/sub>]q\u00d7r<\/sub>
\nOrder of product of AB = p \u00d7 r
\nOrder of product of BA is not defined. Number columns in r is not equal to the number of rows in P.
\n\u2234 Product BA is not defined.<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nA has \u2018a\u2019 rows and \u2018a + 3 \u2019 columns. B has \u20186\u2019 rows and \u201817 – b\u2019 columns, and if both products AB and BA exist, find a, b?
\nSolution:
\nA has a rows, a + 3 columns.
\nB has b rows, 17 – b columns
\nIf AB exists a \u00d7 a + 3
\nb \u00d7 17 – b
\na + 3 = 6 \u21d2 a – 6 = -3 ………… (1)
\nIf BA exists 6 \u00d7 17-6
\na \u00d7 a + 3
\n17 – 6 = a \u21d2 a + 6 = 17 …………. (2)
\n(1) + (2) \u21d2 2a = 14 \u21d2 a = 7
\nSubstitute a = 7 in (1) \u21d2 7 – b = -3 \u21d2 b = 10
\na = 7, b = 10<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nA has \u2018a\u2019 rows and \u2018a + 3 \u2019 columns. B has rows and \u2018b\u2019 columns, and if both products AB and BA exist, find a,b?
\nAnswer:<\/p>\n

    \n
  1. Order of matrix AB = 3 \u00d7 3<\/li>\n
  2. Order of matrix AB = 4 \u00d7 2<\/li>\n
  3. Order of matrix AB = 4 \u00d7 2<\/li>\n
  4. Order of matrix AB = 4 \u00d7 1<\/li>\n
  5. Order of matrix AB = 1 \u00d7 3<\/li>\n<\/ol>\n

    Question 4.
    \n\"Samacheer
    \nfind AB, BA and check if AB = BA?
    \nAnswer:
    \n\"Samacheer<\/p>\n

    Question 5.
    \nGiven that
    \n\"Samacheer
    \n\"Samacheer
    \nverify that A(B + C) = AB + AC
    \nAnswer:
    \n\"Samacheer<\/p>\n

    \"Samacheer
    \n\"Samacheer
    \n\"Samacheer
    \nFrom (1) and (2) we get
    \nA (B + C) = AB + AC<\/p>\n

    \"Samacheer<\/p>\n

    Question 6.
    \nShow that the matrices
    \n\"Samacheer\"Samacheer
    \nsatisfy commutative property AB = BA
    \nAnswer:
    \n\"Samacheer
    \nFrom (1) and (2) we get
    \nAB = BA. It satisfy the commutative property.<\/p>\n

    Question 7.
    \n\"Samacheer
    \nShow that (i) A(BC) = (AB)C
    \n(ii) (A-B)C = AC – BC
    \n(iii) (A-B)T<\/sup> = AT<\/sup> – BT<\/sup>
    \nAnswer:
    \n\"Samacheer
    \n\"Samacheer
    \n\"Samacheer
    \nFrom (1) and (2) we get
    \nA(BC) = (AB)C<\/p>\n

    \"Samacheer
    \n\"Samacheer<\/p>\n

    \"Samacheer<\/p>\n

    From (1) and (2) we get
    \n(A – B) C = AC – BC
    \n\"Samacheer
    \n\"Samacheer
    \nFrom (1) and (2) we get
    \n(A-B)T<\/sup> = AT<\/sup> – BT<\/sup><\/p>\n

    \"Samacheer<\/p>\n

    Question 8.
    \n\"Samacheer
    \nthen snow that A2<\/sup> + B2<\/sup> = I.
    \nAnswer:
    \n\"Samacheer<\/p>\n

    Question 9.
    \n\"Samacheer
    \nprove that AAT<\/sup> = I.
    \nAnswer:
    \n\"Samacheer
    \nAAT<\/sup> = I
    \n\u2234 L.H.S. = R.H.S.<\/p>\n

    \"Samacheer<\/p>\n

    Question 10.
    \nVerify that A2<\/sup> = I when
    \n\"Samacheer
    \nAnswer:
    \n\"Samacheer
    \n\u2234 L.H.S. = R.H.S.<\/p>\n

    Question 11.
    \n\"Samacheer
    \nshow that A2<\/sup> – (a + d)A = (bc – ad)I2<\/sub>.
    \nAnswer:
    \n\"Samacheer
    \nL.H.S. = R.H.S.
    \nA2<\/sup> – (a + d) A = (bc – ad)I2<\/sub><\/p>\n

    \"Samacheer<\/p>\n

    Question 12.
    \n\"Samacheer
    \nverify that (AB)T<\/sup> = BT<\/sup> AT<\/sup>
    \nAnswer:
    \n\"Samacheer
    \n\"Samacheer
    \nFrom (1) and (2) we get, (AB)T<\/sup> = BT<\/sup> AT<\/sup><\/p>\n

    \"Samacheer<\/p>\n

    Question 13.
    \n\"Samacheer
    \nshow that A2<\/sup> – 5A + 7I2<\/sub> = 0
    \nAnswer:
    \n\"Samacheer
    \n\"Samacheer
    \nL.H.S. = R.H.S.
    \n\u2234 A2<\/sup> – 5A + 7I2<\/sub>\u00a0= 0<\/p>\n","protected":false},"excerpt":{"rendered":"

    Students can download Maths Chapter 3 Algebra Ex 3.18 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.18 Question …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/577"}],"collection":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/comments?post=577"}],"version-history":[{"count":1,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/577\/revisions"}],"predecessor-version":[{"id":49456,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/577\/revisions\/49456"}],"wp:attachment":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/media?parent=577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/categories?post=577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/tags?post=577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}