# Determinants Worksheet

### Solutions

1Prove, without developing, that the following determinants are zero:

2Knowing that |A|=5, calculate the value of the other determinants.

3Prove that the following determinants are a multiple of 5 and 4 respectively, without developing them.

4Prove, without developing, that the following determinant is a multiple of 15:

5Prove, without developing.

6 Solve the following equations without developing the determinants.

7If the value of the determinant , calculate the value of:

8Prove that the following determinant is divisible by 21:

## 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.

## 2

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

## 3

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

## 4

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

## 5

Prove, without developing.

## 6

Solve the following equations without developing the determinants.

## 7

If the value of the determinant , calculate the value of:

## 8

Prove that the following determinant is divisible by 21: