Explanation Approach: The determinant is a value assigned to a square matrix. The determinant of a n × n matrix A is denoted by det ( A ) and is given below. det ( A ) = | A | = | a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a n 1 a n 2 ⋯ a n n | = a 11 A 11 + a 12 A 12 + ⋯ + a 1 n A 1 n Where, A 1 n is the n t h cofactor corresponding to the element a 1 n . Applying row or column transformations does not change the value of determinant of a matrix. Calculations: Consider the matrix [ 1 2 0 2 3 − 4 0 4 0 1 6 0 1 0 2 0 ] . Perform the transformation R 2 → R 2 − 2 R 1 . | 1 2 0 2 3 − 2 − 4 − 4 0 4 − 4 0 1 6 0 1 0 2 0 | → | 1 2 0 2 1 − 8 0 0 0 1 6 0 1 0 2 0 | Expand the determinant by fourth column. det ( A ) = ( − 2 ) | 1 − 8 0 0 1 6 1 0 2 | + 0 − 0 + 0 = ( − 2 ) | 1 − 8 0 0 1 6 1 0 2 | Let the obtained 3 × 3 matrix be B

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ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 11.4, Problem 28E

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The determinant of the matrix [12023−40401601020] and check whether the matrix is invertible.

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Chapter 11.4, Problem 27E

Chapter 11.4, Problem 29E

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The determinant of the matrix [ 1 2 0 2 3 − 4 0 4 0 1 6 0 1 0 2 0 ] and check whether the matrix is invertible.

Solution Summary: The author explains that the determinant of the matrix left is 92 and its inverse exists.

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To find:

The determinant of the matrix [12023−40401601020] and check whether the matrix is invertible.

Want to see the full answer?

Chapter 11 Solutions

The determinant of the matrix [ 1 2 0 2 3 − 4 0 4 0 1 6 0 1 0 2 0 ] and check whether the matrix is invertible.

Solution Summary: The author explains that the determinant of the matrix left is 92 and its inverse exists.

Videos

To find: The determinant of the matrix [12023−40401601020] and check whether the matrix is invertible.

Want to see the full answer?

Chapter 11 Solutions

To find:

The determinant of the matrix [12023−40401601020] and check whether the matrix is invertible.