{"id":2409,"date":"2023-11-22T12:28:23","date_gmt":"2023-11-22T06:58:23","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=2409"},"modified":"2023-11-23T15:41:04","modified_gmt":"2023-11-23T10:11:04","slug":"samacheer-kalvi-11th-maths-solutions-chapter-7-ex-7-3","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-11th-maths-solutions-chapter-7-ex-7-3\/","title":{"rendered":"Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.3"},"content":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.3<\/h2>\n

Solve the following problems by using factor theorem<\/p>\n

Question 1.
\nShow that <\"Samacheer = (x – a)2<\/sup> (x + 2a)
\nSolution:
\n\"Samacheer
\n\u21d2 (x + 2d) is a factor of A.
\nNow degree of \u0394 is 3 (x \u00d7 x \u00d7 x = x3<\/sup>) and we have 3 factors for A
\n\u2234 There can be a constant as a factor for A.
\n(i.e.,) \u0394 = k(x – a)2<\/sup> (x + 2d)
\nequating coefficient of x3<\/sup> on either sides we get k = 1<\/p>\n

\"Samacheer<\/p>\n

\u2234 \u0394 = (x – a)2<\/sup> (x + 2a)<\/p>\n

Question 2.
\nShow that \"Samacheer
\nSolution:
\n\"Samacheer
\nSimilarly b and c are factors of \u0394.
\nThe product of the leading diagonal elements is (b + c) (c + a) (a + b)
\nThe degree is 3. And we got 3 factors for \u0394 \u2234 m = 3 – 3 = 0
\n\u2234 there can be a constant k as a factor for \u0394.
\n\"Samacheer><\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u21d2 x = 0, 0 are roots.
\nNow the degree of the leading diagonal elements is 3.
\n\u2234 the equation is of degree 3, so the roots are 0, 0, – (a + b + c)<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nShow that \"Samacheer = (a + b + c) (a – b) (b – c) (c – a)
\nSolution:
\n\"Samacheer
\n\u21d2 (a – b) is a factor of \u0394.
\nSimilarly (b – c) and (c – a) are factors of \u0394.
\nThe degree of the product of elements along leading diagonal is 1 + 1 + 2 = 4 and we got 3 factors for \u0394. m = 4 – 3 = 1
\n\u2234 There can be one more factor symmetric with a, b, c which is of the form k (a + b + c).
\n\"Samacheer<\/p>\n

Question 5.
\nSolve \"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 6.
\nShow that \"Samacheer = (x – y) (y – z) (z – x)
\nSolution:
\n\"Samacheer
\n\u21d2 (x – y) is a factor of \u0394.
\nSimilarly (y – z) and (z – x) are factors of \u0394.
\nNow degree of \u0394 = 0 + 1 + 2 = 3 and we have 3 factors of \u0394.
\nand so there can be a constant k as a factor of \u0394.
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.3 Additional Problems<\/h3>\n

Question 1.
\nProve that \"Samacheer = (a – b) (b – c) (c – a) (a + b + c).
\nSolution:
\n\"Samacheer
\n\u2234 (a – b) is a factor of \u0394.
\nSimilarly we observe that \u0394 is symmetric in a, b, c by putting b = c, c = a, we get \u0394 = 0. Hence (b – c) and (c – a) are also factors of \u0394.
\n\u2234 The product (a – b) (b – c) (c – a) is a factor of \u0394. The degree of this product is 3. The product of leading diagonal elements is 1. bc3<\/sup>. The degree of this product is 4.
\n\u2234 By cyclic and symmetric properties, the remaining symmetric factor of first degree must be k (a + b + c), where k is any non-zero constant.
\n\"Samacheer<\/p>\n

Question 2.
\nUsing factor method show that \"Samacheer = (a – b) (b – c) (c – a)
\nSolution:
\n\"Samacheer
\n\u21d2 (a – b) is a factor of \u0394.
\nsimilarly (b – c) and (c – a) are factors of \u0394.
\nThe product of leading diagonal elements is bc2<\/sup>. The degree of the product is 1 + 2 = 3.
\n\u2234 there will be three factors for \u0394. We got 3 factors for \u0394 as (a – b), (b – c) and (c – a). Its degree = 3. \u2234 m = 3 – 3 = 0
\n\u2234 there can be a constant k as a factor of \u0394.
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u21d2 (a – b) is a factor of A.
\nSimilarly (b – c) and (c – a) are factors of \u0394.
\nThe degree of \u0394 = 5 and degree of product of factors = 3.
\n\"Samacheer
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.3 Solve the following problems by using factor theorem Question 1. Show that < = …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[7],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/2409"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=2409"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/2409\/revisions"}],"predecessor-version":[{"id":59986,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/2409\/revisions\/59986"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=2409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=2409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=2409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}