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

8th Edition

ISBN: 9780357156100

Author: Ron Larson

Publisher: Cengage Limited

See similar textbooks

Videos

Question

Chapter 3.CR, Problem 14CR

To determine

To calculate:

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.CR, Problem 13CR

Chapter 3.CR, Problem 15CR

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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

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].