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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:

 

 

2. 

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 3

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

 

 

 

 

 

 

 

 

Solution of exercise 4

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

 

 

 

 

Solution of exercise 5

Prove, without developing.

 

 

 

Solution of exercise 6

Solve the following equations without developing the determinants.

 

 

, and

 

 

 

 

Solution of exercise 7

Prove that the following determinant is divisible by 21:

 

 

 

 

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.