Explanation Given: The matrix is [ 3 − 1 2 1 − 2 0 1 − 3 − 1 2 − 3 4 − 2 1 − 2 1 ] . Formula used: If A is a square matrix of order n ≥ 2 , then the determinant of A is the sum of the entries in the first row of A multiplied by their respective cofactors. That is, det ( A ) = | A | = ∑ j = 1 n a 11 C 11 + a 12 C 12 + ........... + a 1 n C 1 n . Expansion by Cofactors Let A be the square matrix of order n . Then the determinant of A is, det ( A ) = | A | = ∑ j = 1 n a i j C i j = a i 1 C i 1 + a i 2 C i 2 + ........... + a i n C i n i th row expansion det ( A ) = | A | = ∑ i = 1 n a i j C i j = a 1 j C 1 j + a 2 j C 2 j + ........... + a n j C n j j th column expansion Calculation: Consider the given matrix, A = [ 3 − 1 2 1 − 2 0 1 − 3 − 1 2 − 3 4 − 2 1 − 2 1 ] By using first row, | A | = 3 C 11 − 1 C 12 + 2 C 13 + 1 C 14 Now find C 11 , C 12, C 13 and C 14 by eliminating corresponding row and column of A and then evaluate the determinant of the resulting matrix, C 11 = ( − 1 ) 1 + 1 | 0 1 − 3 2 − 3 4 1 − 2 1 | = | 0 1 − 3 2 − 3 4 1 − 2 1 | Expanding the cofactors by first row, C 11 = 0 ( − 1 ) 1 + 1 | − 3 4 − 2 1 | + ( 1 ) ( − 1 ) 1 + 2 | 2 4 1 1 | + ( − 3 ) ( − 1 ) 1 + 3 | 2 − 3 1 − 2 | = 0 + ( − 1 ) ( − 2 ) + ( − 3 ) ( − 1 ) = 0 + 2 + 3 = 5 C 12 = ( − 1 ) 1 + 2 | − 2 1 − 3 − 1 − 3 4 − 2 − 2 1 | = | 2 − 1 3 1 3 − 4 2 2 − 1 | Expanding the cofactors by first row, C 12 = 2 ( − 1 ) 1 + 1 | 3 − 4 2

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ISBN: 9780357156100

Author: Ron Larson

Publisher: Cengage Limited

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Chapter 3.CR, Problem 14CR

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The determinant of the matrix [3−121−201−3−12−34−21−21].

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Chapter 3.CR, Problem 13CR

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Chapter 3 Solutions

Elementary Linear Algebra

Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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The determinant of the matrix [ 3 − 1 2 1 − 2 0 1 − 3 − 1 2 − 3 4 − 2 1 − 2 1 ] .

Solution Summary: The author calculates the determinant of the given matrix by multiplying the entries in the first row of A by their respective cofactors.

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To calculate:

The determinant of the matrix [3−121−201−3−12−34−21−21].

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Chapter 3 Solutions

The determinant of the matrix [ 3 − 1 2 1 − 2 0 1 − 3 − 1 2 − 3 4 − 2 1 − 2 1 ] .

Solution Summary: The author calculates the determinant of the given matrix by multiplying the entries in the first row of A by their respective cofactors.

Videos

To calculate: The determinant of the matrix [3−121−201−3−12−34−21−21].

Want to see the full answer?

Chapter 3 Solutions

To calculate:

The determinant of the matrix [3−121−201−3−12−34−21−21].