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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 calculus harder than linear algebra?
The answer depends very much on your aptitude, and possibly your interest: there are no absolutes. Some people find calculus easy but not linear algebra and others are the opposite.
Kinds of system of linear equation in two variables?
There are three kinds:
- the equations have a unique solution
- the equations have no solution
- the equations have infinitely many solutions.
Is the equation 3x-4 equals 12 linear or non linear?
It is a linear equation.
The highest power of x in the equation is 1 (3x1-4=12) so its "degree" is 1, and equations of "degree 1" are called linear equations.
Why doesn't an equation cross the x-axis when it cannot be factored?
Since I can't show you graphs on Answers I must ask you to visualise a parabola that does cross the x-axis at two points. (It doesn't matter whether the parabola is 'open' at the top or at the bottom.) For example, we could consider the parabola
5x2 + 9x - 2
We find that it crosses the x-axis at x = 1/5 and x = -2. We call these solutions or roots of
5x2 + 9x - 2 = 0, and we can show that each of these solutions can be used to create a factor of the original parabola.
x = 1/5 yields the factor x - 1/5 :
which we demonstrate by dividing 5x2 + 9x - 2 by x - 1/5 to get 5x + 10 even (and we can check that x - 1/5 multiplied by 5x + 10 yields the original parabola).
x = -2 yields the factor x + 2 :
which we again demonstrate by dividing 5x2 + 9x - 2 by x + 2 to get 5x - 1 even.
The point of this is that when a parabola crosses the x-axis it has solutions that yield factors. However, if it doesn't cross the x-axis it cannot have solutions (because it cannot 'equal' zero), and therefore cannot be factored.
How are patterns or methods use to solve problems involving products of two binomials?
By Trowing garbages
How the graph of 2 square root can be used to graph 3 square root?
A graph of a ^2 looks like a capital "U" and a graph of a ^3 looks like "U" but the left side of the "U" is flipped over the x-axis.
There are many different types of equations. Most of the ones you'll come across have some kind of variable in them. That's a letter that stands in for an unknown number. Solving the equation usually means finding out what that number is. This is achieved by getting the variable by itself on one side of the equation. It doesn't matter which side. Since the values on both sides of the equals sign are the same, whatever you do to one side, if you do it to the other, both sides will still be equal. Here's a simple example:
x + 2 = 5
If you subtract two from the left side, you're left with x. If you subtract two from the right side, you're left with 3. The new equation, x = 3, is the solution, but we knew that, since 3 + 2 = 5. Let's add some stuff.
x/2 + 6 = 10
There are two ways to solve this. You can multiply each thing by two, getting x + 12 = 20. Subtracting 12 from both sides leaves x = 8
or
Subtract 6 from both sides, leaving x/2 = 4. Multiplying both sides by 2 leaves x = 8
Note that 10 = 6 + x/2 would give the same result.
It's important to check your work by plugging the number you found into the original equation.
8 divided by 2 equals 4 plus 6 = 10. It checks. That's how you know you found the right number. As you go along, equations will become more complex, but the process is the same.
What the system of linear equation in two variabes which has no solution?
For two linear equations, they are equations representing parallel lines. (The lines must not be concurrent because if they are, you will have an infinite number of solutions.)
For example y = mx + b
and y = mx + c where b and c are different numbers are two non-concurrent parallel lines. The equations have no solution.
With more than two linear equations there is much more scope. Unless ALL the lines meet at one point, the system will not have a solution. So a system consisting of equations defining the three lines of a triangle, for example, will not have a solution.
There is no "this statement" associated with the question, but the maximum number of points which lie of the graph of a linear equation in two variables is infinite.
Whats the definition of inequality?
An inequality is a relationship between two quantities that are not the same.
How can you tell when an equation has a solution of no solution?
If one side is like this: 0=2 then no it is not equal to in this case you would do a 0 with a line through it. If it is like this: 2=2, or x=2 then it is equal to.
P.S. If it is like this 2=2 then its called the identity property.
How do you do Linear and Exponential Equations?
That completely depends on exactly what operation you have in mind. You can "do"
several different types of operations to an equation, such as solve it, differentiate it,
rearrange it, factor it, or apply the same arithmetic procedure to both sides of it. But
you can't "do" the equation.
Is 2y equals 6x plus 8 the same as y equals 3x plus 6?
Well lets see:
2y = 6x+8
y=3x+4 does not equal y=3x+6
So they are not the same.
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals".
How do you type exponents on a computer?
In text you need to change the font to superscript.
In spreadsheets you use the ^ symbol. So 46 would be entered as "=4^6".
What is the importance of equality?
It did not mean everyone was entitled to have equal amounts of income, housing, personal possessions, health care, etc. Only the opportunity to create those things for yourself.
I've focused on OPPORTUNITY because so many today think it's fine to have the government steal someone else money that may have a little more than others and distribute it to any one the government considers economically challenged, which as we all know may or may not be true.
So please when you are looking at equality, it doesn't mean what the liberal left today would have you believe. Equality only gives you the OPPORTUNITY to be the best you can be, not to provide you with the wear-with-all to reach that goal.
We live in the greatest country in the world, bar none. More people are attempting to get into our country because of this freedom of Opportunity than any other country in the world. This is because of our free enterprise system that allows anyone with the desire to work at any job or become any thing they want to work to attain. Equality does not mean this will be handed to them at the pleasure of the Government, only that each individual can create and reap the rewards of their creation, without government interference.
ANSWER
although it may sound like the poster above is saying equality is an American thing, which is what i picked up on when i read it, it of course is not
equality is in any modern and or westernized countrys, not just America,
the importance of equality is simply to ensure that all people have the same rights as each other person, that no person with any difference, no person with any disability, no race, no sex, no man woman or child would be treated any different to any other man woman or child, in any country.
it keeps the balance of people who may have been successful at something but simply hadn't enough money to study the subject in equal relation to those that were rich or financially stable enough to do so.
so basically poor people can study the same things as rich people which means more success for the country as a whole and not just to the individual. this is one of the most important reasons for this kind of equality
in Britain, technically all people should be treated the same, of course it doesn't work out that way, as there are homeless people, poor people, people without help or love or money, same as in America, same as any country and those people rarely ever get the equal treatment and equal help that everyone person gets, and it doesn't always mean that they didn't take the opportunity, sometimes they weren't given the opportunity to begin with.
in Britain we do all have the same health care, and get help from the government ie financialy as they recognise that it is actually needed to enable the person to acutaly have the opportunity to better themselves and if this wasnt done, if this help wasnt available then many people would never be given or get the opportunity in the first place and it is the opportunity that's important not how you got it
Americas rules and views on equality obviously differ to Britain's, which tells you that everyone has too many different views on what equality is, what makes a person have equality which is why equality will never work properly.
equality in any country does not give everyone the same rights, although it should, it is true as the above poster said that it is about being given the chance to make your life better etc, but anyone who cant do that is given no real chances or help to make their life better, that's not really equality then is it?
equality real, true equality would be that everyone would be given the opportunity to better themselves and their lifes and help when its needed but this is not the case and there will always be people that society pretends don't exist, don't want to help, judge and leave 'out in the cold'
equality is still an ideal not a fact
f4
ANSWER
Equality is a legal concept and has no practicality outside of the law. That we are all equal under the law, regardless of our citizenship status, is what allows us to enjoy our individual natural rights and the inequality of people outside of the law is what makes us so successful in terms of evolution. We can not demand equality of others outside of the law without first doing away with the concept of equality under the law. Equality under the law means no one is above the law, and no one can abrogate or derogate the rights of others. Wealth and poverty are inequalities that exist outside of the law just as ugly and beauty do. To attempt to legislate equality of economics is no different than attempting to legislate plainness as an aesthetic. There will always be inequality of wealth and inequality of beauty, under the law there will never be inequality of justice. Any injustice presented as law is not law and is only simulation of law. People should celebrate both the equality of justice and the inequalities of human nature.
Nine less than three times a number is forty?
Let the number be x:-
3x -9 = 40
3x = 40+9
3x = 49
x = 16 and 1/3
122,312,085,000
When did linear equation use in first time?
no one really knows how did it came into use as there is no written evidences.
Show me a real life hyperbolas application?
The arc of a football when it is kicked is a hyperbola. The arch of a water spout from a hose.
Some think the gateway arch is a hyperbola but it is a centenary arch which is close but just a little different.
What is the x- and y intercept of the linear function 4x12 3y?
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