MYTUTOR SUBJECT ANSWERS

185 views

How do I multiply two matrices together?

In order to multiply two matrices together, you must first have that the number of columns in the first matrix must be equal to the the number of rows in the second matrix.

So if you wish to multiply matrix A and matrix B,

matrix A must have dimensions ( m x n ) whilst matrix B must have dimensions ​(​n ​x q) . Once you multiply these matrices, the new matrix formed will have dimension m xq​ .

(Note that m and q can be equal)

For example, matrix A can have dimension 3x2 and matrix B can have dimension 2x4 and so the new matrix will have dimension 3x4.

To multiply matrices, you take the first row of Matrix A and multiply its elements by the elements in the first column of Matrix B. You then take the first row of Matrix A and multiply its elements by the elements in the second column of Matrix B. You then keep repeating this process till you have multiplied the elements of the first row of Matrix A to the elements of  every single column of Matrix B.

You then take the second row of Matrix A and multiply its elements by the elements of the first column of Matrix B. You then take the second row of Matrix A and multiply it by the elements of the second column of Matrix B. You keep doing this till you have multiplied the second row of Matrix A by every single column of matrix B.

You then repeat this process for the third, fourth, fifth (and so on...) row of matrix A.  The following example should make this clear.

EXAMPLE

​Matrix A is ( A B )    and Matrix B is ( 1 2 3 4 )

                     ( C D )                                   ( 5 6 7 8) 

The dimension of A is 2x2 and the dimension of B is 2x4. Hence, the dimension of the new matrix shall be 2x4.

Using the above rules, it should be simple to follow that new matrix is:

[ (1a+5b)   (2a+6b)   (3a+7b)  (4a+8b) ​]

[ (​1c+5d  ​(​2c+6d)​   (3c+7d)   (4c+8d) ​]

Also note that matrix A multiplied by matrix B does not yield the same result as matrix B multiplied by matrix A. The order in which you multiply matrices matters.

Iretunde S. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tut...

4 months ago

Answered by Iretunde, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

296 SUBJECT SPECIALISTS

£22 /hr

Greg C.

Degree: Economics with Econometrics (Bachelors) - Exeter University

Subjects offered:Maths, Further Mathematics + 2 more

Maths
Further Mathematics
English
-Personal Statements-

“I consider myself a very extrinsic, hardworking person. I like to get involved in as much as I can and this is another opportunity to try something new! At the University of Exeter I’ve involved myself in a vast range of societies inc...”

MyTutor guarantee

£22 /hr

Chris S.

Degree: Psychology (Bachelors) - Nottingham University

Subjects offered:Maths, Psychology+ 1 more

Maths
Psychology
-Personal Statements-

“*Over 25 completed MyTutor school tutorials* I am a reliable and enthusiastic maths and psychology tutor.”

£20 /hr

Tim W.

Degree: BSc Mathematics (Bachelors) - Cardiff University

Subjects offered:Maths

Maths

“I am a mathematics student at Cardiff University and a friendly individual who is very patient. I have been teaching classical guitar for a year to a range of ages from 8 to 15 and so have experience as a teacher.”

About the author

£20 /hr

Iretunde S.

Degree: Mathematics with Economics (Bachelors) - LSE University

Subjects offered:Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find dy/dx where y=e^(4xtanx)

Differentiate y=(x^2+5)^7

Why is the derivative of x^2 equal to 2x?

How do I differentiate implicitly?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok