Maths: Matricies 9.12.21

Addition: 

Matrices are identified by using: [ ] with 4 numbers, two on top of each other. To solve two matrices is to add the opposing numbers in both matrices.


Subtraction:
To take matrices away you have to change the second matricide to a negative value of it and then change the operation sign to an add.

 Division:
To divide you need to multiply the inverse of a matrix. You start by inversing the second matrix.
[3  1]  / [5  7]         so for a 2x2 matrice we start by swapping the first and last numbers 
[12 4] / [6  8]         and putting negatives in front of the second and third numbers.

[5  7]  would be [8  -7]        you then have to divide every entry by what is called the 
[6  8]                 [-6   5]        determinant. To find the determinant you have to take the first and                                            last entries (a and d), multiply them together and subtract the                                                   second and third entries (b and c) multiplied together, so, ad-bc.

Applying this gives you (8*5)-(-7*-6) = 40- 42= -2
Now we divide every entry by that number, -2.            [-4   3.5]
                                                                                     [3   -2.5]

[12 5] / [17  2]  = [8   -2] = (8*17)-(-2*-2) = 136-4 = 132
[6   3]   [2    8]     [-2 17]


Practice Question:

[3 6 9] x [4 12   8   9]  =  [264 382 312 147]
              [6 14 15 17] 
              [24 30 22 2]

[4 12 13] x [9  18] = [316 248]
[34 17 8]    [19  6]    [661 778]
                  [4    8]

[16  17] x [14 15 17] = [530 291 357]
[18  19]    [18   3   5]    [594 327 401]

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