0 A Review Of Basic Algebra 1 Equations And Inequalities 2 Functions And Graphs 3 Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Linear Systems 7 Conic Sections And Quadratic Systems 8 Sequences, Series, And Probability Chapter6: Linear Systems
6.1 Systems Of Linear Equations 6.2 Guassian Elimination And Matrix Methods 6.3 Matrix Algebra 6.4 Matrix Inversion 6.5 Determinants 6.6 Partial Fractions 6.7 Graphs Of Inequalities 6.8 Linear Programming 6.CR Chapter Review 6.CT Chapter Test Section6.5: Determinants
Problem 1SC: Self Check Evaluate 3-25-4 Problem 2SC: In A=123456789 Self Check Find the cofactor of a23. Problem 3SC Problem 4SC Problem 5SC Problem 6SC Problem 7SC: Use Cramers rule to solve 2x-y+2z=6x-y+z=2x+y+2z=9. Problem 8SC: Self Check Find an equation in standard form of line passing through 1,3 and 3,5. Problem 9SC: Self Check Find the area of triangle with vertices at 1,2,2,3 and -1,4. Problem 1E Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E: Practice Evaluate each determinant. 21-23 Problem 8E: Practice Evaluate each determinant. -3-62-5 Problem 9E: Practice Evaluate each determinant. 2-3-35 Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E: In Exercises 11-18, A = 1-2345-6-789. Find each minor or cofactor. C32 Problem 19E: Evaluate each determinant by expanding by cofactors. 2-35-21313-2 Problem 20E: Evaluate each determinant by expanding by cofactors. 131-2533-2-2 Problem 21E: Evaluate each determinant by expanding by cofactors. 1-1221311-1 Problem 22E: Evaluate each determinant by expanding by cofactors. 13121-12-11 Problem 23E: Evaluate each determinant by expanding by cofactors. 21-11352-53 Problem 24E: Evaluate each determinant by expanding by cofactors. 31-2-321130 Problem 25E: Evaluate each determinant by expanding by cofactors. 01-3-3522-53 Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E: If abcdefghi=3,find the value of each determinant. a+gb+hc+idefghi Problem 38E: If abcdefghi=3,find the value of each determinant. ghiabcdef Problem 39E: Use Cramers Rule to find the solution of each system, if possible. 3x+2y=72x-3y=-4 Problem 40E: Use Cramers Rule to find the solution of each system, if possible. x-5y=-63x+2y=-1 Problem 41E: Use Cramers Rule to find the solution of each system, if possible. x-y=33x-7y=9 Problem 42E: Use Cramers Rule to find the solution of each system, if possible. 2x-y=-6x+y=0 Problem 43E: Use Cramers Rule to find the solution of each system, if possible. x+2y+z=2x-y+z=2x+y+3z=4 Problem 44E: Use Cramers Rule to find the solution of each system, if possible. x+2y-z=-12x+y-z=1x-3y-5z=17 Problem 45E: Use Cramers Rule to find the solution of each system, if possible. 2x-y+z=53x-3y+2z=10x+3y+z=0 Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E: Ice skating The illustration shows three circles traced out by a figure skater during her... Problem 71E: Explain how to find the determinant of a 22 matrix. Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA. Problem 83E: If A and B are matrices and AB=0, msut |A|=0 or |B|=0? Explain. Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 55E
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Linear Algebra
Unit : Second and third order determinants and their calculation. Replacements. Definition of determinant of order n
Transcribed Image Text: Calculate the following third-order determinants using the triangle and Sarryus rules.
N
a) N +1
N + 2
- N
N + 1
0
N = 13
-3N
9 - N
5 + N
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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