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suppose A is 3×3 and the following row operations transform A into I₃: - R₂ ⟷R₃ ​ - then 2R₁ +R₃ ⟶R₃ - then 3R₃→R₃ ​ . Find A⁻¹ .

User Aureo Beck
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Final answer:

To find the inverse of Matrix A, perform the row operations described in the question in reverse order. Start with the identity matrix and perform the inverse operations to obtain the A-1, which is the inverse of Matrix A.

Step-by-step explanation:

The question is related to the field of Matrix Algebra, particularly the concept of finding the inverse of a matrix. Here, we are given that matrix A is transformed into the identity matrix (I₃) through a series of row operations, and we are asked to determine the inverse of matrix A based on these operations.

To find the inverse matrix A-1, we will perform the described operations in reverse. Specifically, we start with the identity matrix I₃ and then replicate the inverse operations on I₃ to find A-1.

The operations in reverse order are : - 1/3R₃ → R₃ - (2R₁ -R₃) ⟵ R₃ and finally R₂ ⟷ R₃

We perform these operations on the identity matrix (I₃) to obtain A-1 = Inverse of Matrix A.

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User HRM
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