Q13. Determine whether each pair of m... [FREE SOLUTION]

Chapter 4: Q13. (page 199)

Determine whether each pair of matrices are inverses.13.
$X = [\begin{matrix} \frac{1}{3} & - \frac{2}{3} \\ \frac{2}{3} & - \frac{1}{3} \end{matrix}]$
$Y = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$

Short Answer

Expert verified

The given matrices are not inverse of each other.

Step by step solution

- Definition of inverse of matrix.

A square matrixB is said to be an inverse of the square matrixA if $AB = BA = I$ whereL is an identity matrix of the same order as that of matrixA orB .

- Find the product of the given matrices.

The product of the given matrices is:

$\begin{matrix} X 鈰� Y = [\begin{matrix} \frac{1}{3} & 鈭� \frac{2}{3} \\ \frac{2}{3} & 鈭� \frac{1}{3} \end{matrix}] 鈰� [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}] \\ = [\begin{matrix} (\frac{1}{3}) (1) + (鈭� \frac{2}{3}) (2) & (\frac{1}{3}) (2) + (鈭� \frac{2}{3}) (1) \\ (\frac{2}{3}) (1) + (鈭� \frac{1}{3}) (2) & (\frac{2}{3}) (2) + (鈭� \frac{1}{3}) (1) \end{matrix}] \\ = [\begin{matrix} \frac{1}{3} + (\frac{鈭� 4}{3}) & \frac{2}{3} + (鈭� \frac{2}{3}) \\ \frac{2}{3} + (鈭� \frac{2}{3}) & \frac{4}{3} + (\frac{鈭� 1}{3}) \end{matrix}] \\ = [\begin{matrix} \frac{1}{3} 鈭� \frac{4}{3} & \frac{2}{3} 鈭� \frac{2}{3} \\ \frac{2}{3} 鈭� \frac{2}{3} & \frac{4}{3} 鈭� \frac{1}{3} \end{matrix}] \\ = [\begin{matrix} \frac{1 鈭� 4}{3} & 0 \\ 0 & \frac{4 鈭� 1}{3} \end{matrix}] \\ = [\begin{matrix} \frac{鈭� 3}{3} & 0 \\ 0 & \frac{3}{3} \end{matrix}] \\ = [\begin{matrix} 鈭� 1 & 0 \\ 0 & 1 \end{matrix}] \end{matrix}$

As the product of the given matrices is not equal to the identity matrix, therefore the given matrices are not inverse of each other.

- Write the conclusion.

The given matrices are not inverse of each other.

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

Determine whether each pair of matrices are inverses.13.
$X = [\begin{matrix} \frac{1}{3} & - \frac{2}{3} \\ \frac{2}{3} & - \frac{1}{3} \end{matrix}]$
$Y = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$

Short Answer

Step by step solution

- Definition of inverse of matrix.

- Find the product of the given matrices.

- Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Determine whether each pair of matrices are inverses.13.X=[13-2323-13]Y=[1221]

Short Answer

Step by step solution

­- Definition of inverse of matrix.

­- Find the product of the given matrices.

­- Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Determine whether each pair of matrices are inverses.13.
$X = [\begin{matrix} \frac{1}{3} & - \frac{2}{3} \\ \frac{2}{3} & - \frac{1}{3} \end{matrix}]$
$Y = [\begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}]$

- Definition of inverse of matrix.

- Find the product of the given matrices.

- Write the conclusion.