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Choose to use the traditional printable version, or the paperless, digital Google Apps Mae ices Columns, Rows, Entries Columns 594 Rows s 218 2 by 3 matrix Entry, Session Objectives Determinant of a Square Matrix Minors and Cofactors Properties of Determinants Applications of Determinants Area of a Triangle Solution of System of Linear Equations (Cramer's Rule) Class Exercise, Determinants If A then IAI all If A = a21 is a square matrix of order 1, all is a square matrix of order 2, then a22 alla22 a21a12, Example 4 Evaluate the determinant : 2 5 4 Solution : 2 — 20+6 = 26 5, Solution If A = all a31 all a31 a22 a22 an a13 a23 a33 al 3 a23 a33 is a square matrix of order 3, then a22 = all a32 a23 a21 a23 a21 a22 a33 a31 a33 a31 a32 [Expanding along first row = all (a 22 a33 )-a12 a a a3F23 21 33 31 23 21 32 a31a22 11 22 33 12 31 23 13 21 32 11 23 32 12 21 33 13 31 2, Example Evaluate the determinant : Solution : 7 -3 4 [Expanding along first row] = + 8) -3(7 - 6) - +3) = 18-3-155, Minors -1 If A = 2 4 then 3 = Minor of all Mil — Minor of a21 M21 - = Minor of an M12 — Minor of an = -1 M22 -. 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Atleast two periods per week for this subject. The PowerPoint PPT presentation: "cbse" is the property of its rightful owner. 1 1 x x x x x O [Applying R2 -»R2 -RI and R3 -R2 ] 9 [Expanding along Cl], Example - 10 Show that (c+a)2 a c bc ca ab bc ca ab a c bc ca ab = (a2 +b2 +c2)(a-b)(b-c)(c-a)(a+b+c) Solution : L.H.S.= (c+a)2 a c a c bc ca [Applying Cl ab -2C31 a 1 1 [Applying Cl bc ca ab, Solution Cont. If all the elements of a row (or column) is multiplied by a non-zero number k, then the value of the new determinant is k times the value of the original determinant. CBSE Class 12 Result 2018, Central Board of Secondary Education - CBSE Result 2018, - CBSE 12th Result 2018 - CBSE Board 12th Exam 2018 will be conducted from 5th March to 13th April 2018. A mathematics themed PowerPoint Template to add some creativity to your classroom PowerPoint presentations. Free PowerPoint Presentations about Word Problems for Kids & Teachers (K-12) 7. For CBSE Class 10 students, it provides a comprehensive study package for CBSE Class 10. 2x 1 2x O [Applying R 2 -RI and R 3 Now expanding along Cl , we get =R.H.S, Example -9 Using properties of determinants, prove that x+9 x x x x x+9 x x x+9 = 243 (x+3) Solution : L.H.S= X x x X x X x x x x [Applying C 1 .+C2 + C 3], Solution Cont. Solutions of all questions and examples are given.In this Chapter, we studyWhat aRelationis, Difference between relations and functions and finding relationThen, we defineEmpty and Universal Relationand take some examplesWe study dif CBSE 10th Result 2018, Central Board of Secondary Education - CBSE Result 2018, - CBSE 10th Result 2018 - CBSE Board 10th Exam 2018 will be conducted from 5th March to 4th April 2018. Addition Patterns & Mental Math for Addition. units 2, condition or Collinearity of Three ( 'L) and C ( ')/3) are three points, then A, B, C are collinear Area of triangle ABC — Xl Yl 1 1 1 1, Example If the points (x, -2) , (5, 2), (8, 8) are collinear, find x , using determinants. This is a fun, concise, 16-slide PowerPoint presentation on the properties of real numbers. If D O, then the system has only trivial solution x = y = z (ii) If D = O, then the system has infinite solutions. lesson 1- intro. It includes study materials and online tutorials to help students attain conceptual clarity. Cramer's Rule (Con.) 03.0 03.0 03.0 03.0 Cl and C2 are identical], Example-6 b c c Prove that : a Solution : L.H.S= b b c c b c c [Applying C 1 .+C2 ] b 1 c c 1 [Taking (x+a+b+c) common from, Solution cont. 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