Definition Simply put, a matrix is a rectangular table of numbers that can be added and !multiplied. A 2 2 matrix is a table that consists of two rows and two columns, consisting of four entries. Here are two 2 x 2 matrices, ml and m2 in standard form: and m2= In in-line notation, ml = { {1,2).(3,4)) and m2-((43), (2,1)). Definition Addition When adding two matrices, add corresponding entries. Here is how ml +m2 is determined: Definition Multiplication When multiplying two matrices, to determine the 3]+[:]-[..] . .3 1 entry on the row i column j of the product, the entries of row i in the first matrix re multiplied by the elements of cohumn j of the second matrix pair-wise and the sum of the products is the entry on row i column j of the matrix product. Here is how a matrix product is determined: ae + bg af +bh ce + dg cf dh [3 [:]=[ ,] Here is how m1 m2 is determined: 20 13 Definition The determinant of a 2 x 2 matrix is deternined by multiply- ing the top-left and bottom-right entries and subtracting the product of the top-right and bottom-left entry from it. For example, the determinant of mil, denoted (m1), is l 4-2 3 =-2. Definition The rank of a matrix is the number of linearly independent columns that it has. The rank of a 2 x 2 matrix is 0 when all its entries are 0, 1 when its determinant is 0 and its entries are not all 0, and 2 when its determinant is non-zero. Definition The inverse of a 2 2 matrix is determined by swapping the top- left and bottom-right entries, negating the top-right and bottom-left entries and dividing these four entries by the determinant of the matrix. If the de- terminant of a matrix is 0, its inverse is indeterminate. Here is how a matrix inverse is determined: -1-13(m) | So, m1-1=11.5-0.5 Cl (m)