   Chapter 11.4, Problem 40E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Determinant of a Special Matrix Find the determinant of a 10 × 10 matrix which has a 2 in a each main diagonal entry and zeroes everywhere else.

To determine

To find:

The determinant of a 10×10 matrix which has a 2 in each main diagonal entry and zeroes everywhere else.

Explanation

Approach:

If A is an n×n matrix, then the determinant of A is obtained by multiplying each element of the first row by its cofactor and then adding the results. In symbols,

det(A)=|A|=|a11a12a1na21a22a2nan1an2ann|=a11A11+a12A12++a1nA1n

Calculation:

Consider the 10×10 matrix A=

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