What is the correct way to multiply matrices?

[i.l]

Hey,

When trying to multiply the 2 attached matrixes (row X column) I get a much more terms then the attached answer.
C is for cos and s for sin.
What am I doing wrong?
Regards,
i.l

 

[elibj123]

You mean you don't have terms canceling out?

I suggest working carefully and invoking some trigonometric identities.

 

[Mark44]

I get it that c stands for cosine and s stands for sine, but what does c₁ mean? Cosine of what? Sine of what?

In one of your multiplications you have c₁ in one matrix and c₂ in the other, and you wrote the product as c₁₂. What does that mean?

 

[Simon_Tyler]

Simply typing it into Mathematica and using FullSimplify gets the results that you want. It is merely a combination of trig identities - namely the http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities".

The tricky bit is in the top 2*2 block - I suggest you look at the math for multiplying 2d rotation matrices.

$$A(\text{x\_})\text{:=}\left( \begin{array}{cccc} \cos (x) & -\sin (x) & 0 & a(x) \cos (x) \\ \sin (x) & \cos (x) & 0 & a(x) \sin (x) \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right)$$

$$A(x).A(y)=\left( \begin{array}{cccc} \cos (x+y) & -\sin (x+y) & 0 & a(x) \cos (x)+a(y) \cos (x+y) \\ \sin (x+y) & \cos (x+y) & 0 & a(x) \sin (x)+a(y) \sin (x+y) \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right)$$

 

[blue_raver22]

Hi i.l,

Thank you for reaching out. Matrix multiplication can be a tricky concept, so let's go through it step by step.

First, it's important to make sure that the number of columns in the first matrix matches the number of rows in the second matrix. In your case, both matrixes have 3 columns, so that's good.

Next, when multiplying the matrices, you need to multiply each element in the first row of the first matrix by the corresponding element in the first column of the second matrix, and then add those products together. This will give you the first element in the resulting matrix.

For example, in the first element of your answer matrix, you have C1C1 + C2S1 + C3S2. This comes from multiplying the first row of the first matrix (C1, C2, C3) by the first column of the second matrix (C1, S1, S2).

Then, for the second element in the resulting matrix, you would multiply the first row of the first matrix by the second column of the second matrix, and so on until you have multiplied each row of the first matrix by each column of the second matrix.

It's important to be careful with the order of multiplication, as it can make a big difference in the resulting matrix.

I hope this helps clarify the process. If you're still having trouble, I would recommend reviewing some examples and practicing with smaller matrices before tackling larger ones.

Best regards,