Explanation Given: The matrix is [ 1 2 − 1 3 4 2 3 − 1 2 − 2 1 2 0 1 − 1 1 0 2 − 1 0 0 − 1 1 0 2 ] . Formula: 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 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 Calculation: By using last row, | A | = 0 C 51 − 1 C 52 + 1 C 53 + 0 C 54 + 2 C 55 = − 1 C 52 + 1 C 53 + 2 C 55 Now, find C 52 , C 53 and C 55 by eliminating corresponding row and column of A and then evaluate the determinant of the resulting matrix. C 52 = ( − 1 ) 5 + 2 | 1 − 1 3 4 2 1 2 − 2 1 0 1 − 1 1 2 − 1 0 | = | − 1 1 − 3 − 4 − 2 − 1 − 2 2 − 1 0 − 1 1 − 1 − 2 1 0 | Expanding the cofactors by third row, C 52 = ( − 1 ) ( − 1 ) 3 + 1 | 1 − 3 − 4 − 1 − 2 2 − 2 1 0 | + 0 ( − 1 ) 3 + 2 | − 1 − 3 − 4 − 2 − 2 2 − 1 1 0 | + ( − 1 ) ( − 1 ) 3 + 3 | − 1 1 − 4 − 2 − 1 2 1 − 2 0 | + ( 1 ) ( − 1 ) 3 + 4 | − 1 1 − 3 − 2 − 1 − 2 − 1 − 2 1 | = ( 2 ) | − 3 − 4 − 2 2 | + 1 | 1 − 4 − 1 2 | − 0 | 1 − 3 − 1 − 2 | + 0 − 1 |

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

8th Edition

ISBN: 9781337604925

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 3.CR, Problem 16CR

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The determinant of the matrix, [12−13423−12−21201−1102−100−1102].

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Chapter 3.CR, Problem 15CR

Chapter 3.CR, Problem 17CR

Chapter 3 Solutions

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

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, [ 1 2 − 1 3 4 2 3 − 1 2 − 2 1 2 0 1 − 1 1 0 2 − 1 0 0 − 1 1 0 2 ] .

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, [12−13423−12−21201−1102−100−1102].

Want to see the full answer?

Chapter 3 Solutions

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

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, [12−13423−12−21201−1102−100−1102].

Want to see the full answer?

Chapter 3 Solutions

To calculate:

The determinant of the matrix, [12−13423−12−21201−1102−100−1102].