{"id":24882,"date":"2024-10-16T11:27:16","date_gmt":"2024-10-16T05:57:16","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=24882"},"modified":"2024-10-17T09:46:30","modified_gmt":"2024-10-17T04:16:30","slug":"samacheer-kalvi-11th-maths-guide-chapter-7-ex-7-4","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-11th-maths-guide-chapter-7-ex-7-4\/","title":{"rendered":"Samacheer Kalvi 11th Maths Guide Chapter 7 Matrices and Determinants Ex 7.4"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide<\/a> Pdf Chapter 7 Matrices and Determinants Ex 7.4 Text Book Back Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4<\/h2>\n

Question 1.
\nFind the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
\nAnswer:
\nThe given points are (0, 0), (1, 2) and (4, 3)
\nArea of the triangle with vertices
\n(x1<\/sub>, y1<\/sub>), (x2<\/sub>, y2<\/sub>) and (x3<\/sub>, y3<\/sub>) is
\n\"Samacheer
\n\u2234 The area of the triangle with vertices
\n(0, 0), (1, 2) and (4, 3) is
\n\"Samacheer
\nArea cannot be negative. Taking positive value, we have
\nRequired area \u0394 = \\(\\frac{5}{2}\\) sq.units.<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k.
\nAnswer:
\nGiven Area of the triangle with vertices (k, 2), (2, 4) and (3, 2) is 4 square units.
\nThe area of the triangle with vertices
\n(x1<\/sub>, y1<\/sub>) , (x2<\/sub>, y2<\/sub>) and (x3<\/sub>, y3<\/sub>) is
\n\"Samacheer
\nGiven \u0394 = 4, (x1<\/sub>, y1<\/sub>) = (k , 2), (x2<\/sub>, y2<\/sub>) = (2 , 4) and (x3<\/sub>, y3<\/sub>) = (3 , 2)
\n\"Samacheer
\n\u00b1 4 = k(4 – 2) – 2 (2 – 3) + 1(4 – 12)
\n\u00b1 4 = k \u00d7 2 – 2 \u00d7 – 1 – 8
\n\u00b1 4 = 2k + 2 – 8
\n\u00b1 4 = 2k – 6
\n2k – 6 = 4 or 2k – 6 = -4
\n2k = 4 + 6 or 2k = – 4 + 6
\n2k = 10 or 2k = 2
\nk = 5 or k = 1
\nRequired values of k are 1, 5.<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nIdentify the singular and non – singular matrices.
\n(i) \\(\\left[ \\begin{matrix} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{matrix} \\right] \\)
\n(ii) \\(\\left[ \\begin{matrix} 2 & -3 & 5 \\\\ 6 & 0 & 4 \\\\ 1 & 5 & -7 \\end{matrix} \\right] \\)
\n(iii) \\(\\left[ \\begin{matrix} 0 & a\\quad -\\quad b & k \\\\ b-\\quad a & 0 & 5 \\\\ -k & -5 & 0 \\end{matrix} \\right] \\)
\nAnswer:
\n(i) \\(\\left[ \\begin{matrix} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{matrix} \\right] \\)
\n\"Samacheer
\n|A| = 1 (45 – 48) – 2(36 – 42) + 3(32 – 35)
\n|Al = – 3 – 2 \u00d7 – 6 + 3 \u00d7 – 3
\n|A| = – 3 + 12 – 9
\n|A| = – 12 + 12 = 0
\n\u2234 A is a singular matrix.<\/p>\n

\"Samacheer<\/p>\n

(ii) \\(\\left[ \\begin{matrix} 2 & -3 & 5 \\\\ 6 & 0 & 4 \\\\ 1 & 5 & -7 \\end{matrix} \\right] \\)
\nAnswer:
\n\"Samacheer
\n|B| = 2(0 – 20) + 3 (- 42 – 4) + 5(30 – 0)
\n|B| = -40 + 3 \u00d7 – 46 + 150
\n|B| = -40 – 138 + 150
\n|B| = -178 + 150 \u2260 0
\n\u2234 B is non singular.<\/p>\n

(iii) \\(\\left[ \\begin{matrix} 0 & a\\quad -\\quad b & k \\\\ b-\\quad a & 0 & 5 \\\\ -k & -5 & 0 \\end{matrix} \\right] \\)
\n\"Samacheer
\n|C| = 0 – (a – b) (0 + 5k) + k(-5 (b – a) – 0)
\n|C| = -5k (a – b) – 5k (b – a)
\n|C| = -5k (a – b) + 5k(a – b)
\n|C| = o
\n\u2234 C is a singular matrix.<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nDetermine the values of a and b so that the following matrices are singular:
\n(i) A = \\(\\left[ \\begin{matrix} 7 & 3 \\\\ -2 & a \\end{matrix} \\right] \\)
\n(ii) B = \\(\\left[ \\begin{matrix} b\\quad -\\quad 1 & 2 & 3 \\\\ 3 & 1 & 2 \\\\ 1 & -2 & 4 \\end{matrix} \\right] \\)
\nAnswer:
\n(i) A = \\(\\left[ \\begin{matrix} 7 & 3 \\\\ -2 & a \\end{matrix} \\right] \\)
\n|A| = \\(\\left[ \\begin{matrix} 7 & 3 \\\\ -2 & a \\end{matrix} \\right] \\)
\n|A| = 7a + 6
\nGiven that A is singular
\n\u2234 |A| = 0
\n7a + 6 = 0 \u21d2 a = \\(\\frac{-6}{7}\\)<\/p>\n

(ii) B = \\(\\left[ \\begin{matrix} b\\quad -\\quad 1 & 2 & 3 \\\\ 3 & 1 & 2 \\\\ 1 & -2 & 4 \\end{matrix} \\right] \\)
\n|B| = \\(\\left[ \\begin{matrix} b\\quad -\\quad 1 & 2 & 3 \\\\ 3 & 1 & 2 \\\\ 1 & -2 & 4 \\end{matrix} \\right] \\)
\n= (b – 1 )(4 + 4) – 2(12 – 2) + 3(- 6 – 1)
\n= 8 (b – 1) – 20 – 21
\n= 8b – 8 – 41
\n|B| = 8b -49
\nGiven that B is singular
\n\u2234 |B| = 0
\n8b – 49 = 0 \u21d2 b = \\(\\frac{49}{8}\\)<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nIf cos 2\u03b8 = 0, determine
\n\"Samacheer
\nAnswer:
\nGiven cos 2\u03b8 = 0
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nFind the value of the product
\n\"Samacheer
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide Pdf Chapter 7 Matrices and Determinants Ex 7.4 Text Book Back Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 Question 1. Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3) …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[6],"tags":[],"class_list":["post-24882","post","type-post","status-publish","format-standard","hentry","category-class-11"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/24882"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=24882"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/24882\/revisions"}],"predecessor-version":[{"id":41311,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/24882\/revisions\/41311"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=24882"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=24882"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=24882"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}