In this lesson, we will learn how to identify elementary matrices and their relation with row operations and how to find the inverse of an elementary matrix.

Q1:

Consider the matrix

𝐴=⎡⎢⎢⎣30−482110−183203−97⎤⎥⎥⎦.

Write the elementary matrix corresponding to the row operation 𝑟↔𝑟.

Derive the subsequent row-equivalent matrix ̃𝐴.

Is it true that multiplying ̃𝐴 by the inverse elementary matrix on the left side will return the original matrix 𝐴?

Q2:

𝐴=13032−9413.

Write the elementary matrix corresponding to the row operation 𝑟→𝑟−3𝑟.

Q3:

𝐴=41−4304221098.

Write the elementary matrix corresponding to the row operation 𝑟→𝑟+12𝑟.

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