   Chapter 11.4, Problem 75E ### 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

# DISCUSS: Matrices with determinant Zero Use the definition of determinant and elementary row and column operations to explain why matrices of the following types have determinant 0.(a) A matrix with a row or column consisting entirely of zeros(b) A matrix with two rows the same or two columns the same(c) A matrix in which one row is a multiple of another row, or one column is a multiple of another column

To determine

(a)

To explain:

The statement “A matrix with a row or column consisting entirely of zeros have determinant 0”.

Explanation

Given:

A matrix with a row or column consisting entirely of zeros have determinant 0.

Approach:

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

Using the above results, if all the elements of a row or a column for a matrix are zero, then the corresponding cofactors are zero.

Let matrix A be given by

A=[abcdef000]

The determinant of the matrix [abcdef000] is given below.

To determine

(b)

To explain:

The statement “A matrix with two rows the same or two columns the same have determinant 0”.

To determine

(c)

To explain:

The statement “A matrix in which one row is a multiple of another row, or one column is a multiple of another column have determinant 0”.

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