Full Portfolio ProjectAlex AbelTable of ContentsTitle 1Table of Contents 2Matrices 3Solving Systems of Equations 4Solving Systems of Equations Contd. 5Matrices Examples 6Matrices Examples Continued 7Set Theory 8Set Theory Examples 9Equations 10Equations 11Examples of Equations 12Functions 13Functions Continued. 14Examples of functions 15Examples of functions Continued. 16MatricesA matrix in mathematics is a rectangular array composed primarily of numbers arranged in rows and columns. All individual numbers in the matrix are called elements or entries. Dies date back to the 17th century. The beginning of matrices began during the study of systems of linear equations due to matrices helping in the solution of these equations. Back then, matrices were still known as arrays. Matrices can be added, subtracted and multiplied but with different rules. When adding and subtracting, the matrices must be the same size to be solved. With multiplication, you first need to find the dimensions and make sure the inner numbers match. If so, you then multiply each row by column. There are also three other ways to work with matrices: determinants, special multiplication, and inverses. For determinants, you have variables: A, B, C and D. Remember: you can only find a determinant for square matrices, i.e. 2x2. You will then put in terms “change and deny”. You change variables A and D, cancel B and C, then subtract. After finding this information, you will put your determinant under 1 and solve. Special multiplication is simply taking a ...... middle of paper ...... or odd, and positive or negative before you can determine your answer. Third, you need to see whether your graph is above or below the x-axis between your x-intercepts and insert a value between these intercepts into your function. Last but not least, you plot your graph. Example functions 1.) Relation: {(1,4) , (8, 2) , (7, 3) , (9, 6)} Domain: (1, 8, 7, 9) Range: ( 4, 2, 3, 6)2.) Relation: {(2, c) , (4, b) , (6, a)}Domain range2 a4 b6 c3.) f(x) = 4x2 + 8x + 3-8 / 2 (4) = -1K = 4(-1)2 + 8(-1) + 3  4 – 8 + 3  K = -1Verx (-1, -1)Arrows of this problem will increase because the first number of the The equation is positive. [examples continued on next page]0 = 4x2 + 8x + 3M: 12A: 8  (x-6) (x-2) = 0X-interceptions  (6,0) (2,0)Y = 4(0 )2 + 8(0) + 3  Intercept Y = (0, 3)  [then you plot]5.) f(x) = 4 – 2x2Standard form: -2x2 + 4Degree: 2