All-you-need-to-know-about-matrices in MM CAS Title says it all What are matrices? In Methods CAS, there are three different uses of matrices you need to worry about: 1. Transformation matrices, you only need to know dilation/reflection and translations, which involves a 2D transformation matrix and a 2D vector matrix (EASY) 2. Markov chain using transformation matrices, you don't actually need to know this way, as you can do it the old fashioned way, but it is a lot quicker. In a general sense, it will be a 2x2 Markov chain, some textbooks give 3x3 cases, tell the book to go sholve it (EASY) 3. Solving simultaneous equations (you don't need to know how, you only need to know how to write it and then ask TI for "rref") (EASY) So, it's all easy, but before we begin: Beginner's matrices What are matrices? A matrix is (in some sense) representations of a few vectors in one, but MM'ers don't need to know that. You just need to know, it's a bunch of numbers organised in some kind of rectangles with square brackets There is such thing called "order" for matrices, that is just how many rows you have and how many columns you have (but again, you don't need to know how to express these). In MM, there are two types of matrices you will deal with (with operations): A 2x2 matrix, and easily enough: 1 2] 13 4. 2 A 1x2 matrix, it is As for the matrices you use in rref, you don't need to know how they work, so long as you can interpret the results. (see your textbook) How to add? To add, first make sure that the matrices have the exact same order, they must be in the exact same format. And simply add the numbers together: [2]+ [2]= [2] Mao Yuan Liu - Page 1 of 11
In MM CAS, that is the only addition you will need to be making - 1x2 matrices adding together. Matrix additions are: Commutative: A + B = B + A Associative: (A + B) + C = A + (B + C) So basically matrix addition is normal addition. How to multiply? This is a bit trickier. The key note here is row times column, in that exact order. [3 4] first row x lone column Lsecond row x lone column. 6 So, this would turn into If you have done vectors, what is meant by row x column is basically the dot product of two vectors written differently. If you haven't done vectors before, it's just each element in the row multiplied by its corresponding element in the column and added together: × 6] = [20] Or graphically demonstrating this: [ 2][5] = [1 x 5 + 2 × 6] [17] 3 x 5 + 4 x 6] [29 [1] 13- 21[5] 41 16J 1 × 5 + 2 × 6] L3 x 5 + 4 x 6] L29. [17] Key note here is since multiplication is row