matricies

 

• A matrix  (whose plural is matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
• A matrix with $m$ rows and $n$ columns is called an $m\times n$ matrix or $m$-by-$n$ matrix, where $m$ and $n$ are called the matrix dimensions.
• Matrices can be used to compactly write and work with multiple linear equations, that is, a system of linear equations. Matrices and matrix multiplication reveal their essential features when related to linear transformations, also known as linear maps.
  

subtraction

division

start by inversing the second matrix

so for a 2x2 matrix we start by swapping the first and last number and putting negatives in front of the second and third numbers

[5  7]

[6  8]

would become 

[8  -7]

[-6  5]

you then have to divide every entry by what is called the deterinant

finding the determinant is just simple maths applied to the matrix you just inverted

what we want is to take the first and last entries (a and a) multiply them together and subtract the second and third entries (b and c) multiplied together as well

in algebra it looks like this ad-bc

applying that to our matrix gives you (8x5)-(7x-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 questions

[3  6  9] x [4  12  8  9]      

                [6  14  15 17]  =   [264  382  312  147]        

                [24 30  22 2]

[4  12  13]    [9  18      

[34  17  8] x [19  6] = [316  248]

                    [4  8]      [661 778]

[16  17]    [14  15  17] = 

[18  19] x [18  3  5]