   Chapter 11.4, Problem 39E ### 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

# Calculating a Determinant in Different Ways Consider the matrix B = [ 4 1 0 − 2 − 1 1 4 0 3 ] (a) Evaluate det ( B ) by expanding by the second row.(b) Evaluate det ( B ) by expanding by the second row.(c) Do your results in parts (a) and (b) agree?

To determine

(a)

To Find:

The determinant of the matrix B= by expanding the second row.

Explanation

Approach:

If A is a square matrix and if the matrix B is obtained from A by adding a multiple of one row to another or a multiple of one column to another, then det(A)=det(B).

Calculation:

Consider the determinant B=.

Expand the determinant by the second row.

det(A)=2|1003|140431|4140|=2<

To determine

(b)

To Find:

The determinant of the matrix B= by expanding the third column.

To determine

(c)

If the results of part (a) and (b) agree.

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