0
Linear Algebra
Linear algebra is the detailed study of vector spaces. With applications in such disparate fields as sociology, economics, computer programming, chemistry, and physics, including its essential role in mathematically describing quantum mechanics and the theory of relativity, linear algebra has become one of the most essential mathematical disciplines for the modern world. Please direct all questions regarding matrices, determinants, eigenvalues, eigenvectors, and linear transformations into this category.
2,176 Questions
Is the solution to a quadratic inequality in one variable always a compound inequality?
Yes - except in extreme cases.
It can be the whole of the Real Numbers: eg x2 > -3
It can be a single point eg x2 ≤ 0 gives x = 0
How do you graph a linear equations in two variables explain?
For each linear equation the procedure is the same:
Suppose the equation is y = mx + c where x and y are the two variables and m and c are two constants.
Set x = 0 so that the equation becomes y = c. Mark the point P = (0, c) on the coordinate plane.
Set y = 0 so the equation becomes 0 = mx + c so that x = -c/m. Mark the point Q = (-m/c, 0) on the plane.
Join PQ with a straight line and extend in both directions.
You may wish to select another value of x (or y), substitute into the equation and solve. This will give the coordinates of a third point, R. The only reason for doing this is that if R is not on the line PQ then you know you have made a mistake.
Repeat for other equations.
Are there any vectors associated with HIV?
The vector is body fluid exchange
Correction:
Bodily fluids are not technically vectors. A vector is a living organism, usually a mosquito or tick, that is capable of transmissing disease. To date, no vectors have been identified as causing HIV infection.
How do you solve a system of linear equations by graphing?
When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables.
If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y).
If the graphs do not cross anywhere (for example, parallel lines) then there is no solution.
If the graphs of two lines end up being the same line, then there are an infinite number of solutions.
You must know how to graph a line in order to use this method.
What are the different types of numbers And where did they originate from?
From the simplest to more complicated, there are:
- N, the set of Natural or counting numbers [0], 1, 2, 3, ...
- Z, the set of all integers, ..., -3, -2, -1, 0, 1, 2, 3, ...
- Q, the set of all rational numbers (Q for quotient). These are numbers of the form p/q where p and q are integers and q is not 0.
- Irrational numbers, such as sqrt(2), e, cuberoot(171/2) and so on. These cannot be expressed in the form of a ratio and so are not rational.
- Transcendental numbers are a special type of irrational numbers. Most well known irrational numbers arise as solutions to [non-constant] polynomials with rational coefficients. However, there are numbers such as pi and e (extremely important to mathematics) which are transcendental.
- R, the set of Real numbers are made up of the rational and irratoinal numbers.
- C, the set of complex numbers. These have a part that is real (as above) and a part that is iaginary - related to the square root of -1.
What is the application of metric spaces in your practical life?
WOW! A LOT OF BIG WORDS! have a pretty wide vocabulary, but this is like college stuff! GOOD LUCK
In case any of the points has been miscalculated you will not have a straight line - alerting to to the fact that there is a mistake.
Which is most likely the first step in solving a system of nonlinear equations by substitution APEX?
Isolating a variable in one of the equations.
How do you solve linear equations using linear combinations?
Solving linear equations using linear combinations basically means adding several equations together so that you can cancel out one variable at a time.
For example, take the following two equations: x+y=5 and x-y=1
If you add them together you get 2x=6 or x=3
Now, put that value of x into the first original equation, 3+y=5 or y=2
Therefore your solution is (3, 2)
But problems are not always so simple.
For example, take the following two equations: 3x+2y=13 and 4x-7y=-2 to make the "y" in these equations cancel out, you must multiply the whole equation by a certain number.
What is the definition of algebra?
Algebra is: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic
2 : any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations often analogous to those of arithmetic
Algebra is adding, subtracting, multipling, and dividing with variable and numbers!
there is a easier way to know what it is just think of the letter as something like a for apple here is a e.g
a=5 and p=6
a=apple and p = pear
2a+2p=22
this means 2xa which is 2x5 and 2xp which is 2x6
the answer of 2a and 2p you add together which would be 10+12 which answer 22 and that is your answer
Linear equations are equations whose only terms are constants and/or single variables raised to the first power. More than one variable is allowed in a linear equation, but it is not allowed to be multiplied with another variable. Constants are allowed to be multiplied to variables in linear equations. These equations are called "linear" due to the fact that their solution set forms a line when represented in classic Euclidean space, e.g. when graphed on the mutually perpendicular x, y, and z axes of the Cartesian coordinate system.
Here are three examples of linear equations:
Slope-intercept form:
y = mx + b, where x is the independent variable, y is the dependent variable, and m and b are constants. This representation of a linear equation is useful because the slope of the line formed by its solution set is m.
Point-slope form:
y - y1 = m(x - x1), where x is the independent variable, y is the dependent variable, and m is the constant slope. The point (x1,y1) is included in this form to explicitly show that the independent distances of x and y between two points are proportional to each other by the proportionality constant, m, the slope.
Intercept form:
x/a + y/b = 1, where x and y are variables and a and b are non-zero constants. This form is useful because the x and y intercepts, i.e. the points on a graph where this line crosses the x and y axes, are a and b, respectively.
What is the dilation of 22 if the scale factor is 2.5?
The dilation of 22 with scale factor 2.5 is 55.
The formula for finding a dilation with a scale factor is x' = kx (k = scale factor), so x' = 2.5(22) = 55.
linear algebra has a no. of applications like in any power plant you put all the variables things in linear equations and change them according to your required output of power plant which is surely be the voltages and currents following in the output circuit.
What is the multiplicative property of equality?
States that two sides of an equation remain equal if multiplied by the same number. usually seen algebraically as: if a = b, then ac = bc this is the property that allows you to "move" a number to the other side of the equation by multiplying or dividing both sides by the same number.
How does the method of substitution work for definite integrals?
You mean 'u' subsititution? It helps you get the anti-derivative easier, therefore allowing you to input values to get the definite integral. I hope I helped :D
y=x^2 * k
k=constant of proportionality
OR
y/x^2 = k
In any addition sum, such as 3 + 4 = 7, the addends, otherwise known as summands, are the numbers which are to be added together to create the sum.
Addends are what you add to create the final answer (the sum). For example, in the problem 9+8=17, 9 and 8 are the addends and 17 is the sum.
