{"id":5230,"date":"2020-09-12T11:10:12","date_gmt":"2020-09-12T11:10:12","guid":{"rendered":"https:\/\/samacheer-kalvi.com\/?p=5230"},"modified":"2021-12-06T16:47:23","modified_gmt":"2021-12-06T11:17:23","slug":"samacheer-kalvi-11th-business-maths-guide-chapter-1-ex-1-3","status":"publish","type":"post","link":"https:\/\/samacheer-kalvi.com\/samacheer-kalvi-11th-business-maths-guide-chapter-1-ex-1-3\/","title":{"rendered":"Samacheer Kalvi 11th Business Maths Guide Chapter 1 Matrices and Determinants Ex 1.3"},"content":{"rendered":"

Students can download 11th Business Maths Chapter 1 Matrices and Determinants Ex 1.3 Questions and Answers, Notes, Samcheer Kalvi 11th Business Maths Guide<\/a>\u00a0Pdf 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 11th Business Maths Solutions Chapter 1 Matrices and Determinants Ex 1.3<\/h2>\n

Samacheer Kalvi 11th Business Maths Matrices and Determinants Ex 1.3 Text Book Back Questions and Answers<\/h3>\n

Question 1.
\nSolve by matrix inversion method: 2x + 3y – 5 = 0; x – 2y + 1 = 0.
\nSolution:
\n2x + 3y = 5
\nx – 2y = -1
\nThe given system can be written as
\n\\(\\left[\\begin{array}{rr}
\n2 & 3 \\\\
\n1 & -2
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n5 \\\\
\n-1
\n\\end{array}\\right]\\)
\nAX = B
\nwhere A = \\(\\left[\\begin{array}{rr}
\n2 & 3 \\\\
\n1 & -2
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{r}
\n5 \\\\
\n-1
\n\\end{array}\\right]\\)
\n|A| = \\(\\left|\\begin{array}{rr}
\n2 & 3 \\\\
\n1 & -2
\n\\end{array}\\right|\\) = -4 – 3 = -7 \u2260 0
\n\u2234 A-1<\/sup> Exists.
\n\"Samacheer
\n\u2234 x = 1, y = 1<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nSolve by matrix inversion method:
\n(i) 3x – y + 2z = 13; 2x + y – z = 3; x + 3y – 5z = -8
\n(ii) x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4
\n(iii) 2x – z = 0; 5x + y = 4; y + 3z = 5
\nSolution:
\n(i) The given system can be written as
\n\\(\\left[\\begin{array}{rrr}
\n3 & -1 & 2 \\\\
\n2 & 1 & -1 \\\\
\n1 & 3 & -5
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n13 \\\\
\n3 \\\\
\n-8
\n\\end{array}\\right]\\)
\nAX = B
\nWhere A = \\(\\left[\\begin{array}{rrr}
\n3 & -1 & 2 \\\\
\n2 & 1 & -1 \\\\
\n1 & 3 & -5
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{r}
\n13 \\\\
\n3 \\\\
\n-8
\n\\end{array}\\right]\\)
\n|A| = \\(\\left|\\begin{array}{rrr}
\n3 & -1 & 2 \\\\
\n2 & 1 & -1 \\\\
\n1 & 3 & -5
\n\\end{array}\\right|\\)
\n= 3(-5 + 3) – (-1) (-10 + 1) + 2 (6 – 1)
\n= 3(-2) + 1(-9) + 2(5)
\n= -6 – 9 + 10
\n= -5
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n3 \\\\
\n-2 \\\\
\n1
\n\\end{array}\\right]\\)
\n\u2234 x = 3, y = -2, z = 1.<\/p>\n

(ii) The given system can be written as
\n\\(\\left[\\begin{array}{rrr}
\n1 & -1 & 2 \\\\
\n2 & 0 & 1 \\\\
\n3 & 2 & 1
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n3 \\\\
\n1 \\\\
\n4
\n\\end{array}\\right]\\)
\nAX = B
\nwhere A = \\(\\left[\\begin{array}{rrr}
\n1 & -1 & 2 \\\\
\n2 & 0 & 1 \\\\
\n3 & 2 & 1
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{l}
\n3 \\\\
\n1 \\\\
\n4
\n\\end{array}\\right]\\)
\n|A| = \\(\\left|\\begin{array}{rrr}
\n1 & -1 & 2 \\\\
\n2 & 0 & 1 \\\\
\n3 & 2 & 1
\n\\end{array}\\right|\\)
\n= 1(0 – 2) – (-1)(2 – 3) + 2(4 – 0)
\n= -2 – (-1)(-1) + 2(4)
\n= -2 – 1 + 8
\n= 5
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n-1 \\\\
\n2 \\\\
\n3
\n\\end{array}\\right]\\)
\nx = -1, y = 2, z = 3.<\/p>\n

\"Samacheer<\/p>\n

(iii) The given system can be written as
\n\\(\\left[\\begin{array}{rrr}
\n2 & 0 & -1 \\\\
\n5 & 1 & 0 \\\\
\n0 & 1 & 3
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n0 \\\\
\n4 \\\\
\n5
\n\\end{array}\\right]\\)
\nAX = B
\nWhere A = \\(\\left[\\begin{array}{rrr}
\n2 & 0 & -1 \\\\
\n5 & 1 & 0 \\\\
\n0 & 1 & 3
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{l}
\n0 \\\\
\n4 \\\\
\n5
\n\\end{array}\\right]\\)
\n|A| = \\(\\left|\\begin{array}{rrr}
\n2 & 0 & -1 \\\\
\n5 & 1 & 0 \\\\
\n0 & 1 & 3
\n\\end{array}\\right|\\)
\n= 2(3 – 0) – 0(15 – 0) – 1(5 – 0)
\n= 2(3) – 0(15) – 1(5)
\n= 6 – 0 – 5
\n= 1
\n\"Samacheer
\n\"Samacheer
\n\u2234 x = 1, y = -1, z = 2.<\/p>\n

Question 3.
\nA salesperson Ravi has the following record of sales for the month of January, February, and March 2009 for three products A, B, and C. He has been paid a commission at a fixed rate per unit but at varying rates for products A, B and C.
\n\"Samacheer
\nFind the rate of commission payable on A, B and C per unit sold using matrix inversion method.
\nSolution:
\nLet x, y and z be the rate of commission for the three products A, B and C respectively.
\n9x + 10y + 2z = 800
\n15x + 5y + 4z = 900
\n6x + 10y + 3z = 850
\nThe given system can be written as
\n\\(\\left[\\begin{array}{rrr}
\n9 & 10 & 2 \\\\
\n15 & 5 & 4 \\\\
\n6 & 10 & 3
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n800 \\\\
\n900 \\\\
\n850
\n\\end{array}\\right]\\)
\nAX = B
\nWhere A = \\(\\left[\\begin{array}{rrr}
\n9 & 10 & 2 \\\\
\n15 & 5 & 4 \\\\
\n6 & 10 & 3
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{l}
\n800 \\\\
\n900 \\\\
\n850
\n\\end{array}\\right]\\)
\nNow, |A| = \\(\\left|\\begin{array}{rrr}
\n9 & 10 & 2 \\\\
\n15 & 5 & 4 \\\\
\n6 & 10 & 3
\n\\end{array}\\right|\\)
\n= \\(9\\left|\\begin{array}{rr}
\n5 & 4 \\\\
\n10 & 3
\n\\end{array}\\right|-10\\left|\\begin{array}{rr}
\n15 & 4 \\\\
\n6 & 3
\n\\end{array}\\right|+2\\left|\\begin{array}{rr}
\n15 & 5 \\\\
\n6 & 10
\n\\end{array}\\right|\\)
\n= 9[15 – 40] – 10(45 – 24) + 2(150 – 30)
\n= 9[-25] – 10[21] + 2[120]
\n= -225 – 210 + 240
\n= -195
\n\"Samacheer
\n\"Samacheer
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n17.948 \\\\
\n43.0769 \\\\
\n103.846
\n\\end{array}\\right]\\)
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{r}
\n17.95 \\\\
\n43.08 \\\\
\n103.85
\n\\end{array}\\right]\\)
\n\u2234 x = 17.95, y = 43.08, z = 103.85
\nThe rate of commission of A, B and C are 17.95, 43.08 and 103.85 respectively.<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nThe prices of three commodities A, B, and C are \u20b9 x, y, and z per unit respectively. P purchases 4 units of C and sells 3 units of A and 5 units of B. Q purchases 3 units of B and sells 2 units of A and 1 unit of C. R purchases 1 unit of A and sells 4 units of B and 6 units of C. In the process P, Q and R earn \u20b9 6,000, \u20b9 5,000 and \u20b9 13,000 respectively. By using the matrix inversion method, find the prices per unit of A, B, and C.
\nSolution:
\nTake selling the units js positive earning and buying the units is negative earning.
\nGiven that
\n3x + 5y – 4z = 6000
\n2x – 3y + z = 5000
\n-1x + 4y + 6z = 13000
\n\"Samacheer
\nThe given statement can be written as
\n\\(\\left(\\begin{array}{rrr}
\n3 & 5 & -4 \\\\
\n2 & -3 & 1 \\\\
\n-1 & 4 & 6
\n\\end{array}\\right)\\left(\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right)=\\left(\\begin{array}{r}
\n6000 \\\\
\n5000 \\\\
\n13000
\n\\end{array}\\right)\\)
\nAX = B
\nWhere A = \\(\\left(\\begin{array}{rrr}
\n3 & 5 & -4 \\\\
\n2 & -3 & 1 \\\\
\n-1 & 4 & 6
\n\\end{array}\\right)\\), X = \\(\\left(\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right)\\) and B = \\(\\left(\\begin{array}{r}
\n6000 \\\\
\n5000 \\\\
\n13000
\n\\end{array}\\right)\\)
\nX = A-1<\/sup>B
\n|A| = \\(\\left|\\begin{array}{rrr}
\n3 & 5 & -4 \\\\
\n2 & -3 & 1 \\\\
\n-1 & 4 & 6
\n\\end{array}\\right|\\)
\n= 3(-18 – 4) – 5(12 + 1) – 4(8 – 3)
\n= 3(-22) – 5(13) – 4(5)
\n= -66 – 65 – 20
\n= -151
\n\"Samacheer
\n\"Samacheer
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n3000 \\\\
\n1000 \\\\
\n2000
\n\\end{array}\\right]\\)
\nThe prices per unit of A, B and C are \u20b9 3000, \u20b9 1000 and \u20b9 2000.<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nThe sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
\nSolution:
\nLet the three numbers be x, y, and z.
\nx + y + z = 20
\n2x + y – z = 23
\n3x + y + z = 46
\nThe given system can be written as
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\nThe numbers are 13, 2, and 5.<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nWeekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
\n\"Samacheer
\nSolution:
\nLet \u20b9 x, \u20b9 y, \u20b9 z be the salary for each type of staff A, B and C.
\n4x + 2y + 3z = 4900
\n3x + 3y + 2z = 4500
\n4x + 3y + 4z = 5800
\nThe given system can be written as
\n\\(\\left[\\begin{array}{lll}
\n4 & 2 & 3 \\\\
\n3 & 3 & 2 \\\\
\n4 & 3 & 4
\n\\end{array}\\right]\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n4900 \\\\
\n4500 \\\\
\n5800
\n\\end{array}\\right]\\)
\nAX = B
\nwhere A = \\(\\left[\\begin{array}{lll}
\n4 & 2 & 3 \\\\
\n3 & 3 & 2 \\\\
\n4 & 3 & 4
\n\\end{array}\\right]\\), X = \\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]\\) and B = \\(\\left[\\begin{array}{c}
\n4900 \\\\
\n4500 \\\\
\n5800
\n\\end{array}\\right]\\)
\n|A| = \\(\\left|\\begin{array}{lll}
\n4 & 2 & 3 \\\\
\n3 & 3 & 2 \\\\
\n4 & 3 & 4
\n\\end{array}\\right|\\)
\n= 4(12 – 6) – 2(12 – 8) + 3(9 – 12)
\n= 4(6) – 2(4) + 3(-3)
\n= 24 – 8 – 9
\n= 7
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\\(\\left[\\begin{array}{l}
\nx \\\\
\ny \\\\
\nz
\n\\end{array}\\right]=\\left[\\begin{array}{l}
\n700 \\\\
\n600 \\\\
\n300
\n\\end{array}\\right]\\)
\n\u2234 Salary for each type of staff A, B and C are \u20b9 700, \u20b9 600 and \u20b9 300.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can download 11th Business Maths Chapter 1 Matrices and Determinants Ex 1.3 Questions and Answers, Notes, Samcheer Kalvi 11th Business Maths Guide\u00a0Pdf 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 11th Business Maths Solutions Chapter …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/5230"}],"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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/comments?post=5230"}],"version-history":[{"count":1,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/5230\/revisions"}],"predecessor-version":[{"id":48989,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/5230\/revisions\/48989"}],"wp:attachment":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/media?parent=5230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/categories?post=5230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/tags?post=5230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}