Comprehensive Portfolio Project
Alex Abel
Table of Contents
Title 1
Table of Contents 2
Matrices 3
Solving Systems of Equations 4
Solving Systems of Equations Cont. 5
Matrices Examples 6
Matrices Examples Cont. 7
Set Theory 8
Set Theory Examples 9
Equations 10
Equations 11
Equation Examples 12
Functions 13
Functions Cont. 14
Function Examples 15
Function Examples Cont. 16
Matrices
A matrix in mathematics is a rectangular array of mainly numbers that are arranged in rows and columns. All of the individual numbers in the matrix are called the elements or entries. Matrices go back to the 17th century. The beginning of matrices started when studying systems of linear equations because of matrices helping in the solutions of those equations. Matrices were always known just as arrays back then. Matrices can be added, subtracted, and multiplied but with different rules. When adding and subtracting, matrices must be the same size in order to be solved. With multiplication, you must first find the dimensions and make sure that the inside numbers match. If they do, 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, meaning 2x2. You will then put “switch and negate” into terms. You switch variables A and D, negate B and C, then subtract. After finding that information, you will put your determinant under 1 and solve. Special multiplication is just taking one ...
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... or odd, and positive or negative before you can determine your answer. Third, you have to see if your graph is above or below the x-axis between your x-intercepts and plug a value between these intercepts into your function. Last but not least, you plot your 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 Range
2 a
4 b
6 c
3.) f(x) = 4x2 + 8x + 3
-8 / 2(4) = -1
K = 4(-1)2 + 8(-1) + 3 4 – 8 + 3 K = -1
Vertex (-1, -1)
This problem’s arrows will go up because the first number in the equation is positive.
[ examples continued on the next page ]
0 = 4x2 + 8x + 3
M: 12
A: 8 (x-6) (x-2) = 0
X-intercepts (6,0) (2,0)
Y = 4(0)2 + 8(0) + 3 Y-intercept = (0, 3) [then you graph]
5.) f(x) = 4 – 2x2
Standard form: -2x2 + 4
Degree: 2
Our predicted points for our data are, (13, -88.57) and (-2, -29.84). These points show the
...th the movie and the book have multiple matrices related with each other exactly the way matrices are related in mathematics. There are different dimensions of matrices in mathematics, and society alike, starting from single family and ending with multidimensional matrices of politics, religion,
Y = sales of firm, X = average height of employees, α = intercept of the regression line,
However, same with Ruisantos, Ritika, Preeti and Prem oscilloscope project could not read negative voltage. Besides, they didn’t include the calculation of frequency, rise time and time period to be displayed on the PC.
The "G.O.A.T.", is coming used term in the sports world meaning, The Greatest of All Time. In the National Basketball Association, when you mention the term, the "G.O.A.T., everyone assumes of one name and one name only, Michael Jordan. Michael Jordan was an innovator of the basketball work and influenced many different people and players that inputted & mimicked Jordan’s style of play and implicated it into their own game. In today's generation, there are several players that many average day people would consider these players on the road to becoming a Jordan type of player, potential or maybe even greater; players that may be able on road to sharing a Michael Jordan type of legacy includes Kobe Bryant, Kevin Durant and LeBron James.
The Matrix is the war between man and machine, and the possibility that reality is a deception. In a sense, the Matrix is a constant struggle of identity and reality. This struggle of identity and reality is based around the character of Thomas Anderson, an ordinary person living a mundane life.
The Matrix, directed by the Wachowski sisters, is a film that discusses free will, artificial intelligence and poses a question: ‘How do we know that our world is real?’ This question is covered in the philosophical branch of epistemology. Epistemology is a component of philosophy that is concerned with the theory of knowledge. The exploration of reality is referenced in the film when Neo discovers he has been living in an artificial world called ‘The Matrix’. He is shocked to learn that the world in which he grew up is a computer program that simulates reality. The questioning of knowledge and its irreversibility provoked by The Matrix invites the audience to wonder whether their own world is an imitation of true reality, thus making it a
as the “r-value” and “r” can be any value between -1 and +1. It can be
Wartenberg addressed the question: “Can philosophy be screened?” (pg. 272) He then used thought experiment as a way that a film can represent philosophy. So what is “thought experiment”? Thought examinations include nonexistent situations in which the audience are asked to envision what things might be similar to if such-and-such were the situation. The individuals who feel that movies can really do philosophy show that fiction films can work as philosophical thought experiments and consequently qualify as philosophical. Wartenberg argues that it some fiction films as working in ways that thought experiments do, and thus they may be seen as doing philosophy. (pg. 276)
slope. I think that out of all the variables, this is the one which is
If you’ve ever had deja vu or felt that something about the world was just off, then you might just be living in the Matrix, a digital reality. At least, that is the case in the movie The Matrix directed by the Wachowski brothers. This movie, released March 1st 1999, takes place in a very distant future after a war between humanity and machines with artificial intelligence. A young man named Thomas Anderson, who goes by Neo in his nightlife as a hacker, discovers that the world is not all he thought it to be. Neo learns the truth about his world and what he has to do to save it in this action packed science fiction film.
The Matrix was set in both the present and futuristic time period. The Matrix is an alternate reality where everyone views the world the same except for a few. Neo, the main character of the story, finds himself speaking to Morpheus who asks him to take a red or blue pill. The two pills allow a person to see which reality they want to see. The red pill shows the real world which is in futuristic times where machines control the world, the blue pill allows us to live in the blissful ignorance we live in today. Neo and his fellow team can get back in the world by hooking up to a computer system which acts almost as a virtual reality video game. The antagonist in the movie is Agent Smith, who is an AI program bent on destroying anyone who would
whereβ the intercept 0 and β the slope 1 are unknown constants and ε is a random error component .