Matrix.md (750B)
1 # Matrix 2 3 Khan 4 5 **Definition** A matrix is a 2d grid of numerical values. 6 7 Matricies can be used to describe systems of equations as follows: 8 9 4x - 2y = 10 10 -2x + y = 2 11 12 [4 -2] [x] = [0] 13 [-2 1] [y] = [3] 14 15 This is the form because we distribute x on the first column and y on the second column. 16 17 ## Matrix Vector Product 18 19 The product of a matrix and a vector is another vector of the same size as the original vector. This assumes the number of components in the vector is the same as the number of columns in the matrix. 20 21 [a b c] [j] [aj bk cl] 22 [d e f] @ [k] = [dj ek fl] (note the result is a vector not a matrix) 23 [g h i] [l] [gj hk il] 24 25 This can be thought of as the dot product of each row placed into the correct row as the only column.