Chapter 4: Q4. (page 199)

Determine whether each pair of matrices are inverses.
4. $A = [\begin{matrix} 2 & - 1 \\ 1 & - 3 \end{matrix}]$ ,width="124" height="90" role="math">B=1200-13

Short Answer

Expert verified

The given matrices are not inverse of each other.

Step by step solution

Step 1 - Definition of inverse of matrix.

A square matrix $B$ is said to be an inverse of the square matrix $A$ if $AB = BA = I$ where $I$ is an identity matrix of the same order as that of matrix $A$ or $B$

- Find the product of the given matrices.

The product of the given matrices is:

\begin{matrix} A \cdot B = [\begin{matrix} 2 & - 1 \\ 1 & - 3 \end{matrix}] \cdot [\begin{matrix} \frac{1}{2} & 0 \\ 0 & - \frac{1}{3} \end{matrix}] \\ = [\begin{matrix} (2) (\frac{1}{2}) + (- 1) (0) & (2) (0) + (- 1) (- \frac{1}{3}) \\ (1) (\frac{1}{2}) + (- 3) (0) & (1) (0) + (- 3) (\frac{- 1}{3}) \end{matrix}] \\ = [\begin{matrix} 1 + 0 & 0 + \frac{1}{3} \\ \frac{1}{2} + 0 & 0 + 1 \end{matrix}] \\ = [\begin{matrix} 1 & \frac{1}{3} \\ \frac{1}{2} & 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Determine whether each pair of matrices are inverses.
4. $A = [\begin{matrix} 2 & - 1 \\ 1 & - 3 \end{matrix}]$ ,width="124" height="90" role="math">B=1200-13

Short Answer

Step by step solution

Step 1 - 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

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether each pair of matrices are inverses.4. A=2-11-3,width="124" height="90" role="math">B=1200-13

Short Answer

Step by step solution

Step 1 ­- 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

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether each pair of matrices are inverses.
4. $A = [\begin{matrix} 2 & - 1 \\ 1 & - 3 \end{matrix}]$ ,width="124" height="90" role="math">B=1200-13

Step 1 - Definition of inverse of matrix.

- Find the product of the given matrices.

- Write the conclusion.