September 1, 2020

Chapters

## Exercise 1

Solve:

## Exercise 2

Solve:

## Exercise 3

Solve:

## Exercise 4

Consider the following system for different values of a and b:

## Exercise 5

Solve:

## Exercise 6

Consider the following system for different values of a and b:

## Exercise 7

Determine for what values of k, the following system has infinite solutions:

## Exercise 8

Solve:

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## Solution of exercise 1

Solve:

If a=, r(A) = r(A')=2, n=3

If , this means that the system is a **consistent independent system**!

## Solution of exercise 2

Solve:

Supposing :

, this means that the system is a **consistent dependent system**!

, supposing

In case, , this means that the system is a **consistent independent system**!

## Solution of exercise 3

Solve:

If

, this means that the system is an **inconsistent system**!

If this means that the system is a **consistent independent system**!

Applying row operation :

## Solution of exercise 4

Consider the following system for different values of a and b:

, this means that the system is a **consistent independent system!**

If :

, this means that the system is an **Inconsistent system!**

Otherwise, this means that the system is a **consistent dependent system!**

If :

, this means that the system is an **Inconsistent system!**

## Solution of exercise 5

Solve:

We will be using row operations:

Finding the value of a from the 3rd row:

In the third row, means that the system is a **consistent dependent system**.

which means **inconsistent system**.

## Solution of exercise 6

Consider the following system for different values of a and b:

Applying these row operations:

, hence it is a **consistent indendent system**

which indicates that the system is an **inconsistent system**

which indicates that the system is a **consistent dependent system**

## Solution of exercise 7

Determine for what values of k, the following system has infinite solutions:

Applying row operations:

* 2 was taken as common and divided by 0

## Solution of exercise 8

Solve:

Applying these row operations:

, this means that the system is an **inconsistent system (for any value of m)**

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