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Chapter 1: Q1.2 24E (page 19)

How many types of 2脳3 matrices in reduced row-echelon form are there?

Short Answer

Expert verified

There are seven types of 2脳3 matrices in reduced row-echelon.

Step by step solution

01

Form of 2×3 matrix

All types of 2脳3 matrices can be written as .

Where a, b, c, d, e, and f are constants.

02

2×3 matrix of reduced echelon form

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

Then we have seven options for that

1. At the place of a and f, we have 1. And at b place, we can have y and all other values are 0.

1y0001

2. At the place of b we have 1. And at the place of c, we have x and all other values are 0.

01x000

3. At the place of c, we have 1. And all other values are 0.

001000

4. At the place of b and f we have 1. And all other values are 0.

010001

5. All entry of the matrix is 0.

000000

6.At the place of a and e, we have 1. And all other values are 0.

100010

7. At the place of a, we have 1. And at the place of c and b, we can have z and k and all other values are 0.

1zk000

Hence, there is total of seven matrices,000000,100010,010001,001000,01x000,1y0001,1zk000.

Where x, y, z and k are constant.

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