Question

Find the inverse of each matrix. $$\left[\begin{array}{ll}2 & 3 \\1 & 1\end{array}\right]$$

   Find the inverse of each matrix.
$$\left[\begin{array}{ll}2 & 3 \\1 & 1\end{array}\right]$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 8, Problem 7

Instant Answer

Solved by Expert Joshua Sieverding

06/15/2020

Step 1

This gives us the following matrix: $$\left[\begin{array}{ll|ll}2 & 3 & 1 & 0 \\1 & 1 & 0 & 1\end{array}\right]$$ Show more…

Show all steps

lock

Thanks for your feedback!

Find the inverse of each matrix. $$\left[\begin{array}{ll}2 & 3 \\1 & 1\end{array}\right]$$

Play audio

Feedback

Powered by NumerAI

Joshua Sieverding and 61 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Matrix Inverse

The matrix inverse of a square matrix A is another matrix, denoted A?¹, such that when multiplied together (A * A?¹ or A?¹ * A) the result is the identity matrix. Finding the inverse is equivalent to 'undoing' the linear transformation that A represents, and it is only defined for non-singular matrices whose determinants are non-zero.

Determinant

The determinant is a scalar attribute of a square matrix that provides important information about the matrix, such as whether an inverse exists. In the context of a 2x2 matrix, the determinant is computed as (ad - bc), and the matrix is invertible only if this value is not equal to zero.

2x2 Matrix Inversion Formula

For a 2x2 matrix, the inverse can be computed directly via a formula that involves the matrix's determinant and an arrangement of its elements. Specifically, if the matrix is [[a, b], [c, d]], its inverse is given by (1/(ad - bc)) times the matrix [[d, -b], [-c, a]], provided that the determinant (ad - bc) is non-zero.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later