MATHEMATICS

MATRIX

What is matrix?

A matrix is a simple mathematical structure that holds numerical information in rectangular form, usually enclosed by a bracket.

What’s special about matrix is the values enclosed in a bracket, which cannot be in another mathematical calculation.

E.G Seyi’s school has its number of students in each of the SS class classified as follows:

Male female

SS1 14 8

SS2 6 12

SS3 21 18

The above information can be represented in matrix form.

Matrix A = 14 8

6 12

21 18

Matrix involves two ways, either the horizontal way or the vertical way.

Where the first row represents SS1, the second represent SS2 and the third SS3. Similarly, the first column is the number of male students and the second column for female students. It is customary to write a matrix in the form:

A = a11 a22 a33

a21 a22 a23

a31 a32 a33

three by three matrix.

B = b11 b12

b21 b22

two by two matrix.

The horizontal components:

a11 a12 a13 , a21 a22 a23 , a31 a32 a33 are the rows.

while the vertical components

a11 or a12 or a13

a21 a22 a23

a31 a32 a33

are the column matrix.

You send #13200 to someone and the money hand, so you were so devastated that you want to cause troubled, in order to pacify this anger of yours the owner gave you #13200 that whenever it enters your account you should send him #13200, who lose or gain.

ADDITION AND SUBSTRACTION OF MATRICES

If A= 7 3 4

8 2 5

4 7 8

B = 3 2 4

4 3 4

8 3 3

Find (i) A+B (ii) A-B

Assuming you saw a question like this in your exam, won’t you be happy, because it is as simple as subtracting it according to how the value is placed in the brackets. It is just like giving you 1+1 won’t you be glad to say 2.

So we have,

A+B = 7+3 3+2 4+4

```
8+4 2+3 4+5
4+8 7+3 8+3
```

= 10 5 8

12 5 9

12 10 11

(ii) A – B = 7-3 3-2 4-4

8-4 2-3 4-5

4-8 7-3 8-3

```
= 4 1 0
4 -1 -1
-4 4 5
```

Again let’s look at

A= 2 4

5

B= 3 4

7 8

C= 2 2

0

D = identity matrix

A+B-C-D

what are you going to do from here, okay i guess solving it one after the other will be better.

A+B = 2 4 + 3 4

3 5 7 8

= 5 8 – C

10 13

= 5 8 – 2 2

10 13 1 0

= 3 6 – D

9 13

= 3 6 – 1 0

9 13 0 1

= 2 6

9 12

Final answer. It’s easy, isn’t it.