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Chapter 1: Q1.2 23E (page 19)

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

Short Answer

Expert verified

There are four type of 3脳2 matrices in reduced row-echelon.

Step by step solution

01

Form of 3×2 matrix

All type of 3脳2 matrix can be written asabcdef

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

02

3×2 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. At the place of b we have 1. And all other values are 0.

010000

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

1y000x

3. At place of a and d we have 1. And all other values are 0.

100100

4. All the values are 0.

000000

Hence, there are four types of 3脳2 matrices in reduced row-echelon.

010000,1y000x,100100,000000

Where x and y are constant.

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