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Let A = IA a O a O O O b O O O b O be a diagonal matrix, then O c O O = abc c, Row(Column) Operations Following are the notations to evaluate a determinant: (i) Ri to denote ith row (ii) to denote the interchange of ith and jth rows. * Decreased liver function Contraindications: This pill must be consumed for 6-12 months for the optimum result. Free powerpoint presentations on Maths. Have your students create reports and presentations that cover all subject areas using PowerPoint. Maths is the study of quantity, area, space, and change. 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. Winner of the Standing Ovation Award for “Best PowerPoint Templates” from Presentations Magazine. Mathematics (12 Slides) R. By: Ravikiran . The Abacus – What Is It? ign ys em or or er and order 3 are given by, Example-I Find the value of the following determinants 42 1 (i) 28 7 14 3 Solution : 6 4 2 6 2 1 7 3 6 2 -10 6 4 2 42 (i) 28 14 = 74 7 = 7 xo 1 7 3 6 4 2 [Taking out 7 common from q] Cl and C3 are identical], Example 6 -10 5 2 3x(-2) -3 1 —3 5 5 -3 -1 5 -1 2 2 2 2 2 2 [Taking out-2 common from Cl ] Cl and C2 are identical], Example - 2 Evaluate the determinant 1 1 C Solution : 1 c a-I-b 1 = (a-I-b+c) I 1 1 1 1 a b c 1 1 1 [Applying —>C2 -I-C3] [Taking (a+b+ c) common from [o: Cl and C3 are identical], Example - 3 Evaluate the determinant: a a bc c 2 c ab b ca Solution: a We have a2 bc (a-b) -c(a-b) b ca 1 -c c 2 c ab b-c -a(b-c) c 2 c ab [Applying — C2 and — 1 -a c 2 c ab Taking (a-b) and (b-c) common from Cl and C2 respectively, Solution Cont. 140 Creative PowerPoint Presentation Topics for College Students. Student Easley understanding of all important concepts covered in each chapter. 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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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