Q11. Evaluate each determinant using ... [FREE SOLUTION]

91影视

Chapter 4: Q11. (page 186)

Evaluate each determinant using expansion by minors.
$|\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}| = 鈭� 43$ .

Step by step solution

- Decide row to use for expansion

In this case, use first row for the expansion by minors.

$|\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}| = 2 |\begin{matrix} 5 & 7 \\ 2 & 8 \end{matrix}| 鈭� 3 |\begin{matrix} 6 & 7 \\ 1 & 8 \end{matrix}| + 4 |\begin{matrix} 6 & 5 \\ 1 & 2 \end{matrix}|$

- Evaluate 2×2 determinants

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d 鈭� b c$ . Apply this definition to find the $2 脳 2$ determinant.

$\begin{matrix} |\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}| = 2 |\begin{matrix} 5 & 7 \\ 2 & 8 \end{matrix}| 鈭� 3 |\begin{matrix} 6 & 7 \\ 1 & 8 \end{matrix}| + 4 |\begin{matrix} 6 & 5 \\ 1 & 2 \end{matrix}| \\ = 2 (40 鈭� 14) 鈭� 3 (48 鈭� 7) + 4 (12 鈭� 5) \end{matrix}$

- Multiply and simplify

Further simplify the values.

$\begin{matrix} |\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}| = 2 (40 鈭� 14) 鈭� 3 (48 鈭� 7) + 4 (12 鈭� 5) \\ = 2 脳 26 鈭� 3 脳 41 + 4 脳 7 \\ = 52 鈭� 123 + 28 \\ = 鈭� 43 \end{matrix}$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate each determinant using expansion by minors.
$|\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}|$

Short Answer

Step by step solution

- Decide row to use for expansion

- Evaluate 2×2 determinants

- Multiply and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Mechanics Maths

Decision Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

Evaluate each determinant using expansion by minors.234657128

Short Answer

Step by step solution

- Decide row to use for expansion

- Evaluate 2×2 determinants

- Multiply and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Mechanics Maths

Decision Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Evaluate each determinant using expansion by minors.
$|\begin{matrix} 2 & 3 & 4 \\ 6 & 5 & 7 \\ 1 & 2 & 8 \end{matrix}|$