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# Calculation of the determinants + verifiation

## 1.

Calculation of the determinants + verifiationa11

a12

a13

a21

a22

a23 a11a22 a33 a12 a23 a31 a12 a32 a13 a31a22 a13 a21a12 a33 a11a32 a23

a31

a32

a33

n

det A aik ( 1)i k det A(i ,k )

k 1

1

## 2.

Dodgson condensationCharles Lutwidge Dodgson

(better known as Lewis Carroll)

2

## 3.

3## 4.

4## 5.

5## 6.

6## 7.

Сonstructive problems on divisibility1. How many zeros ends the number 100!

2. How many six-digit numbers exist in which all digits are odd?

3. How many six-digit numbers exist that have at least one even

digit in the record?

4. Can the sum of 19 consecutive positive integers be divisible by

87?

5. Can the sum of 12 consecutive positive integers be divisible by 4?

7