6.5_bzca5e

# 6.5_bzca5e - We can generalize the idea for fourth-order...

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Section 6.5 Determinants and Cramer’s Rule

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The Determinant of a 2 x 2 Matrix

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Example Evaluate the determinant of each of the following matices: 2 3 . 5 1 3 2 . 4 1 a b - - -
Solving Systems of Linear Equations in Two Variables Using Determinants

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Example Use Cramer's Rule to solve the system: 2x-3y=-11 x+2y=12

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Example Use Cramer's Rule to solve the system: 3x+2y=-1 2x-4y=10
The Determinant of a 3 x 3 Matrix

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Evaluate the determinant of the following matrix: 2 1 0 1 1 2 3 1 0 - - -

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Example Evaluate the determinant by hand, then check your answer on the calculator. 2 1 3 3 0 1 1 2 3 - -
Solving Systems of Linear Equations in Three Variables Using Determinants

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Example Use Cramer's rule to solve: -2x+y =1 x-y-2z=2 3x+y =6

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Cramer’s Rule with Inconsistent and Dependent Systems

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The Determinant of Any N x N Matrix
The determinant of a matrix with n rows and n columns is said to be an nth-order determinant. The value of an nth-order determinant can be found in terms of determinants of order n-1.

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Unformatted text preview: We can generalize the idea for fourth-order determinants and higher. We have seen that the minor of the element a is the determinant obtained by deleting the ith row and the jth column in the given array of numbers i j . The cofactor of the element a is (-1) times the minor of the a entry. If the sum of the row and column (i+j) is even, the cofactor is the same as the minor. If the sum of the row and column i j i j ij th + (i+j) is odd, the cofactor is the opposite of the minor. Example Evaluate the determinant of the following matrix. Notice that you can use either the third or the fourth columns. 1 2 1 2 1 2 1 1 3 1 1 - -- - (a) (b) (c) (d) Evaluate the determinant 3 2 1 4 -- 14 10 8 11----(a) (b) (c) (d) Use Cramer's Rule to solve the linear systems.-x+2y=7 2x-2y=-4 ( 1,2) (2, 2) (3,4) (3,5)--...
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## This document was uploaded on 10/26/2011 for the course FKP bmfp at UTEM Chile.

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6.5_bzca5e - We can generalize the idea for fourth-order...

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