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Determinants
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Determinants

Introduction As we have seen, square matrix is ​​one that has the same number of rows and columns (ie it is of type n x n). Every square matrix is ​​associated with a number which we call the determinant. Among the various applications of determinants in mathematics, we have: solving some types of systems of linear equations; calculating the area of ​​a triangle situated in the Cartesian plane, when the coordinates of its vertices are known; First-order determinant Given a first-order square matrix M = [a 11], its determinant is the real number at 11: det M = Ia 11 I = a 11 Note: We represent the determinant of a matrix between two vertical bars, that do not have the meaning of module.

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What is scale?

In the area of ​​measurement, we say that scale is the constant ratio between any physical or chemical quantity that allows a comparison. In the case of a drawing or map, we call the cartographic scale the mathematical relationship between the dimensions presented in the drawing and the real object it represents. These dimensions should always be taken in the same unit.
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Body surface area

Did you know that dermatologists have come up with a formula to roughly calculate a person's body surface area? The area (in m 2) is calculated as a function of the individual's mass (m): For example, a person with a mass of 70kg has a body surface area of ​​approximately: The resulting value is useful for determining the amount of heat. lost through sweat.
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What are leap years?

A year is leap when it is divisible by 4. But there is one exception. Years ending with two zeros will be leap if they are divisible by 400. Example: 2012 is a leap year. For 2012/4 = 503, that is, an exact division. 1998 is not a leap year, because 1998/4 = 499.5, an inaccurate division.
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What is a capicua number?

A number is capitalized when read from left to right or right-to-left always represents the same value, such as 77, 434, 6446, 82328. To get one number from another, the order of the numbers is reversed. digits and sum with the given number a number of times until a capicua number is found, for example: From the number 84: 84 + 48 = 132; 132 + 231 = 363, which is a capicua number.
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The Easter that happened earlier

Easter 2008 happened very early on March 23rd. In fact, it was earlier than any of us will see during our lives! The last time this happened was in 1913. The next time Easter will take place on March 23, will be in the year 2228. Therefore, we will not be here to witness (at least in this life, for those who thought of reincarnation).
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How much is a cent worth?

The largest number accepted in the system of successive powers of ten is the million, first recorded in 1852. It represents the hundredth power of one million, or the number 1 followed by 600 zeros (although only used in Great Britain and Germany). ). Curiosity with Triangular Numbers Index Next >> Whole Number Squares
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Mega-Seine Odds

Check out the odds you have of winning at Mega-Sena according to the amount of numbers played. Numbers played Probability of Hit (1 in…) Sena Quina Quadra 6 50,063,860 154,518 2,332 7 7,151,980 44,981 1,038 8 1,787,995 17,192 539 9 595,998 7,791 312 10 238,399 3,973 195 11 108.
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Mathematical Pope

Did you know that there was a mathematical Pope? Gerbert, famous geometer, was archbishop of Ravenna and ascended to St. Peter's Chair in the year 999. Considered one of the wisest of his time, he was called Pope Silvester II. It was the first to vulgarize in the Latin West the use of Arabic numerals. In addition to mathematics, he devoted himself to the study of astronomy, physics as well as other sciences under Muslim rule in Spain.
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Tragic death of some mathematicians

Tales of Miletus - asphyxiated by the crowd when leaving a show. Archimedes - murdered by a Roman soldier. Eratosthenes - killed himself, starving himself. Hypatia - cut by a group of exalted people during a mutiny in Alexandria. Évariste Galois - killed in a duel. Pythagoras - assassinated in Tarento during a revolution.
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What is Sudoku?

Sudoku is a fun and addictive game that is turning fever all over the world. The goal of the game is to complete a grid (vertical columns and horizontal lines) by filling in the blanks with numbers from 1 to 9. The secret: the number cannot be repeated in the same column, row or block. Here's an example of Sudoku, with its solution: Solution: Click here to download Sudoku Solver, a puzzle solver software.
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Mathematics Movies

Several films have Mathematics as their theme. Here are some of them: Breaking the Bank ”(USA, 2008), by Robert Luketic. "The Proof" (USA, 2005), by John Madden. "A Bright Mind" (USA, 2005), by Ron Howard. “Enigma” (USA, 2001), by Michael Apted. “Pi” (USA, 1988), by Darren Aronofsky.
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The two inverse operations of potentiation

The inverse operations of potentiation are: root and logarithmization. This is because in the potentiation operation there is no commutativity property. For example: 5 3 = 5 x 5 x 5 = 125 is different from 3 5 = 3 x 3 x 3 x 3 x 3 = 243 By definition, the inverse operation to potentiation consists of: given the power and one of the data, the base or exponent must determine the other.
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Why are antennas satellite dishes?

Satellite dishes have the shape of a curve called a parabola, which is associated with the graph of second degree function. We define parable from a line r and a point F, called focus, in a plane. The focus parable F and guideline r is the set of all points whose distance to the line r is equal to the distance to the point F.
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Mathematical Revolution - Differential and Integral Calculus

The differential and integral calculus, which Newton develops at the same time as the German Wilheim Leibniz (1646-1716), revolutionizes mathematics. To know the area of ​​a circle using the new tool, just divide that circle into even, small squares. Then the area of ​​a square is calculated and multiplied by the total number of squares.
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Challenge 1

The Age Problem Difficulty Level: I'm twice the age you were when I was your age. When you are my age, the sum of our ages will be 45 years. What are our current ages? Challenge Index Next >> Challenge 2 Combinatorial Analysis
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Challenge 101

The damn tomatoes Difficulty level: You have a 2-plate scale and 12 tomatoes, with: - 11 having the same weight - 1 having the different weight (we don't know if it's lighter or heavier) With only three weighings, find out which tomato is different and whether it is lighter or heavier. * challenge sent by user Fábio Gomes Cordeiro.
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The origin of the matrix name

Just over 150 years ago, the matrices had their importance detected and emerged from the shadow of the determinants. The first to give them a name seems to have been Cauchy, 1826: tableau (= table). The parent name only came with James Joseph Sylvester, 1850. His friend Cayley, with his famous 1858 Memoir on the Theory of Matrices, spread the name and began to demonstrate its usefulness.
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Challenge 114

Eight Queens on the Chess Board Difficulty Level: Place 8 queens on a chess board so that one cannot capture the other. Challenge 113 Orlaneide and the Animals Challenge Index Next >> Challenge 115 Half Thirteen
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Challenge 120

Fire in the Rope Difficulty Level: We have two ropes that do not necessarily have the same length. If we set fire to the end of either string, it will take exactly 1 hour for the fire to reach the other end of the string. However, the fire will not move at constant speed, it may be faster at some points and slower at others.
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Challenge 103

Correcting the Expression with a Dash Difficulty Level: Correct the expression below with just one dash: 5 + 5 + 5 = 550 Challenge 102 Serginho Crossing the Bridge Challenge Index Next >> Challenge 104 Clodovando's Father and Grandfather
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