In this lesson, we will learn how to perform elementary row operations on a matrix.

Q1:

Consider the matrix 𝐴=263−1. After obtaining the row-equivalent matrix ̃𝐴 by performing the following elementary row operations in order: 𝑟→12𝑟, 𝑟↔𝑟, 𝑟→𝑟−2𝑟, and 𝑟→𝑟−𝑟, what is the determinant of 𝐴 in terms of the determinant of the row-equivalent matrix ̃𝐴?

Q2:

Consider the matrix 𝐴=15−2201−120. After obtaining the row-equivalent matrix ̃𝐴 by performing the following elementary row operations in order: 𝑟→3𝑟, 𝑟→−2𝑟, 𝑟→𝑟+𝑟, 𝑟↔𝑟, and 𝑟→𝑟−2𝑟, what is the determinant of 𝐴 in terms of the determinant of the row-equivalent matrix ̃𝐴?

Q3:

Consider the matrix 𝐴=13−6021142. Use elementary row operations to reduce the matrix into upper-triangular form.

Calculate the determinant of matrix 𝐴.

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