Q51. Find the inverse of each matrix,... [FREE SOLUTION]

Chapter 12: Q51. (page 637)

Find the inverse of each matrix, if it exists.
$[\begin{matrix} 3 & 1 \\ 鈭� 4 & 1 \end{matrix}]$

Short Answer

Expert verified

The inverse of the given matrix is $[\begin{matrix} \frac{1}{7} & 鈭� \frac{1}{7} \\ \frac{4}{7} & \frac{3}{7} \end{matrix}]$ .

Step by step solution

Step 1. Given Information.

Given, to find the inverse of the matrix $[\begin{matrix} 3 & 1 \\ 鈭� 4 & 1 \end{matrix}]$ .

Step 2. Calculation.

The inverse of matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}] 鈥�$ is $A^{鈭� 1} = \frac{1}{a d 鈭� b c} [\begin{matrix} d & 鈭� b \\ 鈭� c & a \end{matrix}]$ ,where $a d 鈭� b c 鈮� 0$ :

Here $a = 3, b = 1, c = 鈭� 4, d = 1$ .

Checking if the inverse exists:

$\begin{array}{l} a d 鈭� b c = (3) (1) 鈭� (1) (鈭� 4) \\ a d 鈭� b c = 3 + 4 \\ a d 鈭� b c = 7 \end{array}$

Hence, the inverse exists.

The inverse of the given matrix is:

$\begin{array}{l} A^{鈭� 1} = \frac{1}{a d 鈭� b c} [\begin{matrix} d & 鈭� b \\ 鈭� c & a \end{matrix}] \\ A^{鈭� 1} = \frac{1}{(3) (1) 鈭� (1) (鈭� 4)} [\begin{matrix} 1 & 鈭� 1 \\ 鈭� (鈭� 4) & 3 \end{matrix}] \\ A^{鈭� 1} = \frac{1}{3 + 4} [\begin{matrix} 1 & 鈭� 1 \\ 4 & 3 \end{matrix}] \\ A^{鈭� 1} = \frac{1}{7} [\begin{matrix} 1 & 鈭� 1 \\ 4 & 3 \end{matrix}] \\ A^{鈭� 1} = [\begin{matrix} \frac{1}{7} & 鈭� \frac{1}{7} \\ \frac{4}{7} & \frac{3}{7} \end{matrix}] \end{array}$

Step 3. Conclusion.

Hence, the inverse of the given matrix is $[\begin{matrix} \frac{1}{7} & 鈭� \frac{1}{7} \\ \frac{4}{7} & \frac{3}{7} \end{matrix}]$ .

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

Find the inverse of each matrix, if it exists.
$[\begin{matrix} 3 & 1 \\ 鈭� 4 & 1 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

Discrete Mathematics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Find the inverse of each matrix, if it exists.31鈭�41

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

Discrete Mathematics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the inverse of each matrix, if it exists.
$[\begin{matrix} 3 & 1 \\ 鈭� 4 & 1 \end{matrix}]$