The three types of matrix row operations

The three types of matrix row operations

In this section we will learn about matrix row operations. There are three types of matrix row operations: interchanging 2 rows, multiplying a row, and adding/subtracting a row with another. Each notation for this is different, and is displayed in the note section. First, we will look at questions which involve all three types of matrix row operations. Then we will look at more slightly advanced questions that involve using 2 matrix row operations.

Lessons

The first type of matrix row operation is that we are allowed to switch any rows you want. For example,
first type of matrix row operation

We interchanged the row 1 and row 3. Another way of saying this is R1R3R_1\leftrightarrow R_3.

The second type of matrix row operation is that we can multiply a row by a non-zero constant. For example,
second type of matrix row operation

We multiplied each entry in row 1 by 3. Another way of saying this is 3R1R13R_1\leftrightarrow R_1.

The third type of matrix row operation is that we are allowed to add and subtract a row with another. For example,
third type of matrix row operation

Row 2 is the sum of row 2 and 1. Another way of saying this is R1+R2R_1+R_2 R2 R_2.
  • 1.
    Matrix row operations overview:

  • 2.
    One matrix row operation
    You are given the following matrix

    The three types of matrix row operations

    Perform the following matrix operations:
    a)
    R1R2R_1\leftrightarrow R_2

    b)
    R2R3R_2\leftrightarrow R_3

    c)
    4R3-4R_3R3 R_3

    d)
    3R23R_2R2 R_2

    e)
    R1+R2R_1+R_2 R2 R_2

    f)
    R1+R3R_1+R_3 R3 R_3


  • 3.
    More than one matrix row operation
    You are given the following matrix

    The three types of matrix row operations

    Perform the following matrix operations:
    a)
    3R1+2R43R_1+2R_4 R4 R_4

    b)
    2R2R12R_2-R_1 R2 R_2

    c)
    2R3+R1-2R_3+R_1 R1 R_1

    d)
    2R2+2R3-2R_2+2R_3 R3 R_3