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Chapter 1: Q1.2 22E (page 19)

We say that two n脳mmatrices in reduced row-echelon form are of the same type if they contain the same number of leading 1鈥檚 in the same positions. For example,

120001and130001

Are of the same type. How many types of 2脳2 matrices in reduced row-echelon form are there?

Short Answer

Expert verified

There are four type of 2脳2 matrices in reduced row-echelon.

10c0Where c is constant. 0010,1001,0000

Step by step solution

01

Form of 2 × 2 matrix

All type of 2脳2 matrix can be written like

acbdWhere a, b, c, d are constants.

02

2×2 matrix of reduced echelon form

In the above matrix if we want to reduce it to echelon form

Then we have three options for that

1. The first-row first column entry contains 1 and the rest are 0.

10c0

2. The first column contains only 0 and the first-row second entry must be 1.

0010

3. The first entry of row 1 is1and the second entry is 0. The first entry of the first row is 0 and the second entry is 0.

1001

4. All entry of the matrix is 0.

0000

Hence, there are four metrices, that are:10c0,0010,1001 and 0000, Where c is constant.

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