/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 What happens to the value of a s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 73

What happens to the value of a second-order determinant if the two columns are interchanged?

Short Answer

Expert verified
When the two columns of a second-order determinant are swapped, the value of the determinant is negated.

Step by step solution

01

Understand Second Order Determinant

A second order determinant is written in the format: \[ \Delta = \begin{vmatrix} a & b \\ c & d \end{vmatrix}\], and its value is computed as \(ad - bc\).
02

Swapping Columns

If the two columns of this determinant are swapped, then the determinant changes to \[ \Delta = \begin{vmatrix} b & a \\ d & c \end{vmatrix}\]. The value of this new determinant is \(bc - ad\).
03

Compare Values

The value of the new determinant after swapping columns is negative of original second order determinent i.e., \(- \Delta\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the following matrices: a. \(A+B\) b. \(A-B\) c. \(-4 A\) d. \(3 A+2 B\) $$ A=\left[\begin{array}{r} {2} \\ {-4} \\ {1} \end{array}\right], \quad B=\left[\begin{array}{r} {-5} \\ {3} \\ {-1} \end{array}\right] $$

Exercises \(72-74\) will help you prepare for the material covered in the next section. In each exercise, refer to the following system: $$ \left\\{\begin{aligned} 3 x-4 y+4 z &=7 \\ x-y-2 z &=2 \\ 2 x-3 y+6 z &=5 \end{aligned}\right. $$ Show that \((12 z+1,10 z-1, z)\) satisfies the system for \(z=1\)

Solve: \(2 \cos ^{2} x+3 \sin x-3=0, \quad 0 \leq x<2 \pi\)

If two matrices can be multiplied, describe how to determine the order of the product.

Solve: \(\quad 3^{2 x-8}=27 .\) (Section \(4.4,\) Example 1 )
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.