{"id":1146,"date":"2020-02-29T12:12:07","date_gmt":"2020-02-29T12:12:07","guid":{"rendered":"https:\/\/tnboardsolutions.com\/?p=1146"},"modified":"2021-07-08T03:43:06","modified_gmt":"2021-07-08T09:13:06","slug":"samacheer-kalvi-12th-maths-guide-chapter-1-ex-1-5","status":"publish","type":"post","link":"https:\/\/tnboardsolutions.com\/samacheer-kalvi-12th-maths-guide-chapter-1-ex-1-5\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 1 Applications of Matrices and Determinants Ex 1.5"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 1 Applications of Matrices and Determinants Ex 1.5 Textbook Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.5<\/h2>\n

Question 1.
\nSolve the following systems of linear equations by Gaussian elimination method:
\n(i) 2x – 2y + 3z = 2, x + 2y – z = 3, 3x – y + 2z = 1
\nSolution:
\nAugmented matrix
\n\"Samacheer
\nWriting the equivalent equations from echelon from.
\nx – y + 2z = 3 …………. (1)
\n5y – 6z = -4 ………….. (2)
\n-z = -4
\nz = 4
\n(2) \u21d2 5y – 6z = -4
\n5y – 24 = -4
\n5y = -4 + 24
\n5y = 20
\ny = 4
\n(1) \u21d2 x – y + 2z = 3
\nx – 4 + 8 = 3
\nx = 3 + 4 – 8
\nx = -1
\n\u2234 x = -1, y = 4, z = 4<\/p>\n

\"Samacheer<\/p>\n

(ii) 2x + 4y + 6z = 22, 3x + 8y + 5z = 27, -x + y + 2z = 2.
\nSolution:
\nAugmented matrix
\n\"Samacheer
\nWriting the equivalent equations from echelon from.
\nx + 2y + 3z = 11 …………. (1)
\ny – 2z = -3 ………….. (2)
\n11z = 22
\nz = 2
\n(2) \u21d2 y – 2z = -3
\ny – 4 = -3
\ny = -3 + 4
\ny = 1
\n(1) \u21d2 x + 2y + 3z = 11
\nx + 2(1) + 3(2) = 11
\nx + 2 + 6 = 11
\nx = 11 – 8 = 3
\n\u2234 x = 3, y = 1, z = 2<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf ax\u00b2 + bx + c is divided by x + 3, x – 5, and x – 1, the remainders are 21, 61 and 9 respectively. Find a, b and c. (Use Gaussian elimination method.)
\nSolution:
\nGiven: f(x) = ax\u00b2 + bx + c
\nIn Remainder Theorem
\nf(-3) = 21
\na(-3)\u00b2 + b(-3) + c = 21
\n9a – 3b + c = 21 ……….. (1)
\nf(5) = 61
\n25a + 5b + c = 61 …………. (2)
\nf(1) = 9
\na + b + c = 9 ………… (3)
\nAugmented matrix
\n\"Samacheer
\nWriting the equivalent equations from echelon from.
\na + b + c = 9 …………. (1)
\nb + 2c = 5 ………….. (2)
\n-4c = -8
\nc = 2
\n(2) \u21d2 b + 2c = 5
\nb + 4 = 5
\nb = 5 – 4
\nb = 1
\n(1) \u21d2 a + b + c = 9
\na + 1 + 2 = 9
\na = 9 – 3
\na = 6
\na = 6, b = 1, c = 2<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nAn amount of Rs 65,000 is invested in three bonds at the rates of 6%, 8% and 10% per annum respectively. The total annual income is Rs 5,000. The income from the third bond is Rs 800 more than that from the second bond. Determine the price of each bond. (Use Gaussian elimination method.)
\nSolution:
\nLet the amounts of 3 bounds be x, y, z
\nx + y + z = 65,000
\n\"Samacheer
\nWriting the equivalent equations from echelon from.
\nx + y + z = 65000 …………. (1)
\n2y + 3z = 90000 ………….. (2)
\n21z = 42000
\nz = 20000
\n(2) \u21d2 2y = 90000 – 3 \u00d7 20000
\n2y = 30000
\ny = 15000
\n(1) \u21d2 x + 15000 + 20000 = 65000
\nx = 30000
\n\u2234 x = 30000, y = 15000, z = 20000<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nA boy is walking along the path y = ax\u00b2 + bx + c through the points (-6, 8),(-2, -12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? (Use Gaussian elimination method.)
\nSolution:
\ny = ax\u00b2 + bx + c
\nAt(-6, 8) \u21d2 8 = 36a – 6b + c ………… (1)
\nAt(-2, -12) \u21d2 -12 = 4a – 2b + c ………… (2)
\nAt(3, 8) \u21d2 8 = 9a + 3b + c ………… (3)
\nAugmented matrix
\n\"Samacheer
\nWriting the equivalent equations from the echelon.
\n36a – 6b + c = 8 …………. (1)
\n3b – 2c = 29 ………….. (2)
\n5c = -50
\nc = -10
\n(2) \u21d2 3b – 2c = 29
\n3b – 20 = 29
\n3b = 9
\nb = 3
\n(1) \u21d2 36a – 18 – 10 = 8
\n36a = 8 + 18 + 10
\n36a = 36
\na = 1
\nAt P (7, 60), y = ax\u00b2 + bx + c
\n60 = 1(7\u00b2) + 3(7) – 10
\n60 = 49 – 21 – 10
\n60 = 60
\nHe will meet his friend at P (7, 60)<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 1 Applications of Matrices and Determinants Ex 1.5 Textbook Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 1 Applications of Matrices and Determinants Ex 1.5 Question 1. Solve the following systems of linear equations by Gaussian elimination method: (i) 2x – …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/1146"}],"collection":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/comments?post=1146"}],"version-history":[{"count":0,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/posts\/1146\/revisions"}],"wp:attachment":[{"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/media?parent=1146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/categories?post=1146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tnboardsolutions.com\/wp-json\/wp\/v2\/tags?post=1146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}