# Thread: Calculating Matrices?

1. ## Calculating Matrices?

Let

|1 −2 1| = A
|4 −2 3|

|−3 2| = B
| 1 5 |

and

|−1 3 5 |
| 2 4 −1 | = C
| 6 −2 3 |

Using the matrices above labelled A, B, and C above, either calculate the matrices described below, or explain why it is not possible to do so.

a) BA

b) AC − B

c) BAC

*please give ur workings and a clear answer so i can understand it.

2. *please give ur workings and a clear answer so i can understand it.
Well, I'll let you do the actual working, but if I explain how to multiply matrices, then that should help.

Rules:

* To multiply matrices, the number of COLUMNS in the first matrix must EQUAL the number of ROWS in the second one. If not, it's not possible to multiply them, and it makes no sense.

* If you multiply A and B together in that order, that is NOT the same as multiplying B with A. When you switch the order, things change (at least, in general).

* You can only add and subtract matrices when they have the same number of rows and columsn.

* Erm... that'll do for now.

Okay, so on with the lesson.

Multiplying Matrices: Method

To multiply matrices, write them down in the order you're going to multiply them.

* Put your two forefingers on the top left element of both matrices. Multiply them together and remember it.

* Move your left finger to the RIGHT and your right finger DOWN. Multiply the two numbers that you're now on and add that to the number you got before.

* Keep doing this until you have no more numbers. The total of all the numbers you've added up is the TOP LEFT element of the answer.

(See, it takes quite a while to work them out - it's just practice. And trust me with the finger thing - it's the best way.)

To work out the element below the top left element your left forefinger starts one below the top left, and your right forefinger starts at the top.

To work out the element that's to the right of the top left element, you start with your left forefinger in the top left and your right forefinger at the start of the second column in.

i.e. Your left finger starts at the left of the ROW of the element you're trying to work out. You right finger starts at the top of the COLUMN of the element you're trying to work out.

Your left finger works to the right and your right finger works down.

* * * *

That should help you make some progress.

Now, the proper mathematicians will laughing themselves silly now at what I just said, but the finger thing really is the best way. It makes sure that you don't miss any elements and it becomes automatic after a while. It's what I still do in exams anyway.
Just trust me, and try it.