Complete portfolio projectAlex AbelIndexTitle 1Index 2Matrices 3Solving systems of equations 4Solving systems of equations Cont. 5Examples of matrices 6Examples of matrices Cont. 7Set theory 8Examples of set theory 9Equations 10Equations 11Examples of equations 12Functions 13Functions Cont. 14Examples of Functions 15Examples of Functions Cont. 16MatricesA matrix in mathematics is a rectangular matrix composed mainly of numbers arranged in rows and columns. All the individual numbers in the matrix are called elements or entries. The matrices date back to the 17th century. The inception of matrices began during the study of systems of linear equations due to matrices helping in the solutions of such equations. At the time, matrices were always known simply 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 solve. With multiplication, you first need to find the dimensions and make sure the internal numbers match. If they do, you 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. So you will put it in “change and deny” terms. Swap variables A and D, negate B and C, then subtract. After finding this information, you will put your determinant under 1 and solve. Special multiplication involves simply taking one...half of the 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, plot the graph. Function Examples 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 interval2 a4 b6 c3.) f(x) = 4x2 + 8x + 3-8 / 2(4) = -1K = 4(-1)2 + 8(-1) + 3  4 – 8 + 3  K = -1Vertex ( -1, -1)The arrows in this problem will point upwards because the first number in the equation is positive.[examples continued on next page]0 = 4x2 + 8x + 3M: 12A: 8  (x-6) (x-2) = 0X-intercept  (6,0) ( 2,0)Y = 4(0)2 + 8(0) + 3  Y-intercept = (0, 3)  [then graph]5.) f(x) = 4 – 2x2Standard form: -2x2 + 4Rank: 2