# Matrix multiplication question

1. Nov 13, 2008

### transgalactic

i am given two matrices 4X4

which i need to multiply by one another

but in my calculator i can multiply matrices only 3X3

how can i use this maximum 3X3 matrices multiplication
in order to calculate the multiplication of two 4X4 matrices
??
(i know how to multiply matrices in theory but i want to shorten the process)

2. Nov 13, 2008

### HallsofIvy

Staff Emeritus
What in the world kind of calculator is that? The TI-85- 89 calculators have a "matrix editor" that allows you to input the "m by n" dimensions of a matrix. I've never heard of a calculator that allows 3 by 3 matrices but no others!

3. Nov 13, 2008

### transgalactic

my calculator inputs matrices till m<=3 n<=3

i cant multiply 4X4 matrices one by one another
with the help of my calculator.

is there any mathematical methods of solving this without doing the formal way?

using smaller multiplications which could be done in my calculator

4. Nov 13, 2008

### Office_Shredder

Staff Emeritus
If you write each matrix as the sum of four matrices with zeros everywhere except by a 2x2 block in the corner, then you're essentially just multiplying a bunch of 2x2 matrices together along with a lot of distribution, addition and figuring out which corner the product of the matrices has its 2x2 block in. But that sounds like more work than just doing the multiplication... if you practice doing matrix multiplication by hand you get pretty fast at it.

5. Nov 13, 2008

### SNOOTCHIEBOOCHEE

6. Nov 13, 2008

### transgalactic

its for a test purpose in order to save time
can i make a multiplication of two 4X4 matrices using smaller multiplications

7. Nov 15, 2008

### transgalactic

i got a solution
we take the blocks of M1 and M2 (4X4 matrices)
M1 M2

A1 B1 A2 B2
C1 D1 * C2 D2
=
A1*A2+B1*C2 A1*B2+B1*D2
C1*A2+D1*C2 C1*B2+D1*D2

is that correct?