MYTUTOR SUBJECT ANSWERS

228 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...

5 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

270 SUBJECT SPECIALISTS

£20 /hr

Iebad A.

Degree: Aerospace Engineering (Masters) - Sheffield University

Subjects offered:Maths, Italian

Maths
Italian

“About me: Hello, my name is Iebad and I am an aerospace engineering student at The University of Sheffield. As an engineer, maths is the key to unlock all the solutions to our problems in this field. Since the early years I had a broad...”

£22 /hr

Dan B.

Degree: MPhys Physics (Masters) - Exeter University

Subjects offered:Maths, Physics

Maths
Physics

“Hi I'm Dan and I'm in the first year of a four-year MPhys Physics degree at the University of Exeter. I am very patient and will tailor the sessions' content and pace to suit your individual needs...”

£22 /hr

Samuel H.

Degree: Philosophy (Bachelors) - Bristol University

Subjects offered:Maths, Philosophy and Ethics+ 2 more

Maths
Philosophy and Ethics
-Personal Statements-

“Philosophy student specialising in Philosophy of Maths and Science, can provide high quality tuition in these subjects, and assist with personal statements.”

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

How to gain an inverse function

Line AB has the equation 3x + 5y = 7. Find the gradient of Line AB.

The Curve, C, has equation: x^2 - 3xy - 4y^2 +64 =0 Find dy/dx in terms of x and y. [Taken from Edexcel C4 2015 Q6a]

The Chain Rule: Differentiate (x^2 + 1)^5/2 with respect to x

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