Question

Use row reduction to find the inverse of the given matrix if it exists, and check your answer by multiplication.

2 1
1 1
If the inverse doesn't exist, enter DNE in all answer boxes.

Answer 1

Explanation:

Given the 2×2 matrix since the matrix consists of 2rows and 2columns, to find its inverse using row reduction method, we will augment the matrix given with a 2×2 identity matrix before carrying out the reduction on the resulting 2×4 matrices. The resulting matrix must be an identity matrix augmented with the inverse of the matrix in question. The process of reduction is as shown in simple steps.

[A | I] -> [I | A-¹] where

A is the given matrix

I is the 2×2 identity matrix

A-¹ is the inverse of the matrix

Check attachment for the reduced matrix.

Answer 2

Step-by-step explanation: see attachment below