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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
Would you show an example of math how to find the cross product?
For two vectors (A & B) in 3-space, using the (i j k) unit vector notation:
if A = a1*i + a2*j + a3*k, and B = b1*i + b2*j + b3*k the cross product A X B can be found by computing a determinant of the following matrix:
| i j k |
|a1 a2 a3 |
|b1 b2 b3 |
Mathematically, it will look like this: (a2*b3 - a3*b2)*i- (a1*b3 - a3*b1)*j + (a1*b2 - a2*b1)*k
I did do just a little copy/paste from the crossproduct website, which I've posted a link to, which has some good information.
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same.
in simple words,square of the matrix is equal to the same matrix.
if M is our matrix,then
MM=M.
then M is a idempotent matrix.
What happens when Cramer's rule is applied to dependent or inconsistent systems?
We call the coefficients of the variables in the system D, and we need to find the determinant of D. When D = 0, the system is either inconsistent or dependent. You need another method to solve it.
Benefits of Caley hamilton theorem in matrices?
The Cayley-Hamilton (not Caley hamilton) theorem allows powers of the matrix to be calculated more simply by using the characteristic function of the matrix. It can also provide a simple way to calculate the inverse matrix.
He was a sixteenth century mathematician, born in Jawor (now in southwestern Poland) who wrote the first book on algebra in the German language. He studied at the University of Vienna. He invented the symbol we now use for square root, and also was the first to define the zero power to equal one.
What are the first 15 perfect squares?
first 15 r:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, and 225
A scale in Math is used in a chart.
For example, if you wanted to make a chart such as "Tickets Sold", a scale would be usually the number of tickets sold. It is also usually done in a pattern such as 1000, 2000, 3000, 4000, and so on.
A linear system is an equation to find the intersection of two or more lines. The equations are usually expressed with two variables, x and y. I don't know yet, but maybe geometry might have three variables, including z. Basically it's where two lines intersect and the most common ways of solving it are through graphing, substitution, and/or elimination.
Presume you mean "linear".
These are systems whose parameters vary directly or proportionally. Plotting functions results in straight lines.
When you have a fraction on each side of the equals you can multiply the denominator of the left side times the numerator of the right. It will equal the product of the numerator on the left side times the denominator of the right.
That is called cross products.
Identify the degree and leading coefficient of polynomial functions. ... the bird problem, we need to understand a specific type of function. A power ... A power function is a function that can be represented in the form ... Example 3.4.1: Identifying Power Functions ... Comparing Smooth and Continuous Graphs.
Mollweide's formula is used to check the solution of triangles. It is also known as Mollweide's equations. It is named after the a German mathematician, Karl Mollweide.
We use algebra for many reasons and one of them is for replacing knowm values into unknown values
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
How are polynomials used in everyday life?
sometimes they can help to model markets in the business world, but other than that, they just help you get a better understanding of other algebra, some of which you actually do use.
Higher-degree polynomials are pretty well always going to be abstract, but you probably use some of the lower-level ones all the time, without even noticing. Say you've got a box that holds a 6x6 grid of eggs, and two extra eggs that don't fit in it. You could sit there and count the eggs, or you could say if x=6, then x2+2=38.
And admittedly you're probably not asking about linearpolynomials, but they're all over the place.
engineers, every single teacher, chemists, laboratory technicians
A function of the form f(x) = mx + c where m and c are constants is linear.
Hard to tell because of problems with the browser.
If the question is about "y = 0" the answer is YES.
Algebra was my favorite subject and I have found none of its uses helpful to me, but a few of the uses are to find the distance of a bus and when you will arrive by doing the formula D=RxT distance equals rate times time. and finding when the two buses would arrive if they left at the same time if they were going different speeds or if they left at different times going the same speed by using another formula. There are many little things like that that it can be used for, none of which I would exert my time and energy to find out. but you could definitely use algebra for something in life.
-- Amanda
