/*! 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} Q19E Find the determinant in Exercise... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q19E (page 165)

Find the determinant in Exercise 19, where \[\left| {\begin{aligned}{*{20}{c}}{\bf{a}}&{\bf{b}}&{\bf{c}}\\{\bf{d}}&{\bf{e}}&{\bf{f}}\\{\bf{g}}&{\bf{h}}&{\bf{i}}\end{aligned}} \right| = {\bf{7}}\].

19. \[\left| {\begin{aligned}{*{20}{c}}{\bf{a}}&{\bf{b}}&{\bf{c}}\\{{\bf{2d}} + {\bf{a}}}&{{\bf{2e}} + {\bf{b}}}&{{\bf{2f}} + {\bf{c}}}\\{\bf{g}}&{\bf{h}}&{\bf{i}}\end{aligned}} \right|\]

Short Answer

Expert verified

Hence, \[\left| {\begin{aligned}{*{20}{c}}a&b&c\\{2d + a}&{2e + b}&{2f + c}\\g&h&i\end{aligned}} \right| = 14\].

Step by step solution

01

Reduce the given determinant

At row 2, add \[ - 1\] time row 1 to row 2 to obtain:

\[\begin{aligned}{c}\left| {\begin{aligned}{*{20}{c}}a&b&c\\{2d + a}&{2e + b}&{2f + c}\\g&h&i\end{aligned}} \right| = \left| {\begin{aligned}{*{20}{c}}a&b&c\\{2d}&{2e}&{2f}\\g&h&i\end{aligned}} \right|\\ = 2\left| {\begin{aligned}{*{20}{c}}a&b&c\\d&e&f\\g&h&i\end{aligned}} \right|\end{aligned}\]

02

Use the given statement

The given statement is \[\left| {\begin{aligned}{*{20}{c}}a&b&c\\d&e&f\\g&h&i\end{aligned}} \right| = 7\].

03

Conclusion

Therefore,

\[\begin{aligned}{c}\left| {\begin{aligned}{*{20}{c}}a&b&c\\{2d + a}&{2e + b}&{2f + c}\\g&h&i\end{aligned}} \right| = 2\left( 7 \right)\\ = 14\end{aligned}\]

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

Question: In Exercise 20, find the area of the parallelogram whose vertices are listed.

20. \(\left( {0,0} \right),\left( { - {\bf{2}},4} \right),\left( {4, - 5} \right),\left( {2, - 1} \right)\)

In Exercise 19-24, explore the effect of an elementary row operation on the determinant of a matrix. In each case, state the row operation and describe how it affects the determinant.

\(\left[ {\begin{array}{*{20}{c}}a&b&c\\{\bf{3}}&{\bf{2}}&{\bf{1}}\\{\bf{4}}&{\bf{5}}&{\bf{6}}\end{array}} \right],\left[ {\begin{array}{*{20}{c}}{\bf{3}}&{\bf{2}}&{\bf{1}}\\a&b&c\\{\bf{4}}&{\bf{5}}&{\bf{6}}\end{array}} \right]\)

Compute \(det{\rm{ }}{B^4}\), where \(B = \left[ {\begin{aligned}{{}{}}1&0&1\\1&1&2\\1&2&1\end{aligned}} \right]\).

In Exercises 31-36, mention an appropriate theorem in your explanation.

36. Find a formula for \(\det \left( {rA} \right)\) when \(A\) is an\(n \times n\) matrix.

Compute the determinants of the elementary matrices given in Exercise 25-30.

26. \(\left[ {\begin{aligned}{*{20}{c}}0&0&1\\0&1&0\\1&0&0\end{aligned}} \right]\).
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.