Chapters

## Exercise 1

Prove, without developing, that the following determinants are zero:

## Exercise 2

Knowing that |A|=5, calculate the value of the other determinants.

## Exercise 3

Prove that the following determinants are a multiple of 5 and 4 respectively, without developing them.

## Exercise 4

Prove, without developing, that the following determinant is a multiple of 15:

## Exercise 5

Prove, without developing.

## Exercise 6

Solve the following equations without developing the determinants.

## Exercise 7

Prove that the following determinant is divisible by 21:

,

## Solution of exercise 1

Prove, without developing, that the following determinants are zero:

It has two proportional lines. The third column equals the sum of the first two.

## Solution of exercise 2

Knowing that |A|=5, calculate the value of the other determinants.

## Solution of exercise 7

Prove that the following determinant is divisible by 21:

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