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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
How to download Linear Algebra A Geometric Approach by s kumaresan for free?
i wish to download linear algebra a geometrical approach by s kumareson
What is the difference between abstract algebra and linear algebra?
Linear algebra concerns vector spaces whether finite- or infinite-dimensional. Abstract algebra, or modern algebra, includes linear algebra, along with many other kinds of objects, such as groups, rings, fields, lattices, and so on. In part, it was an attempt to put mathematics on a more rigorous footing.
Please see the links.
What are two possible uses for physics equations?
Using information about a force to calculate the resulting acceleration..Using the change in the volume of a gas to calculate the change in its pressure.
How do you describe a product matrix without multiplying?
You can indicate the multiplication with a multiplication sign. If your matrices are "A" and "B", the product is:
A x B
In other words, you are indicating the product, but not actually carrying out any multiplication. Anybody who understands about matrices should know what this refers to.
Why can't linear graphs give an idea with clothing sizes for infants?
Growth rates of children is not a linear relationship. (The rate of growth changes at different ages).
Methods on system of linear equations?
Let
- y be the column vector the dependent variable,
- M be the matrix of coefficients, and
- x be the column vector of variables
Then the solution set is obtained by left-multiplying both sides by M^-1
that is x = M^-1*y
How do you find a linear equation?
You have to solve it or if the answer is provided to you look at the y axis which is the one on the right of the graph. If the numbers form a pattern then its linear if there not... Well you can figure that out. It works for me most of the time and on a test one of five was wrong on this method.
How do you find rank of a matrix?
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix.
Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
How do you solve the equation -( x plus 4 ) 8?
Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see of the so called equation is "-( x plus 4 ) 8?". From that it is not at all clear where the missing symbols might be.
Assuming that the question is about -( x plus 4 ) =8,
then multiply both sides by -1 to give x + 4 = -8
next subtract 4 from both sides so that x = -12
Done!
When does the nonlinear equation becomes linear equation?
A linear equation is defined as an equation that contains only the first power of the unknown quantity.
For example, 5x - 3 = 7 where "x" is the unknown quantity is a linear equation.
If an equation contains an unknown quantity having a higher power than 1, then the equation ceases to be a linear equation.
For example, 3x2 + 5x + 7 = 0 is a non linear equation known as a quadratic equation, because the unknown quantity "x" has a power of 2.
Similarly, equations containing unknowns with higher powers such as x3, x7, x12 are all non linear equations.
How do you create a Linear Equation using data?
There are two cases to consider. The first is one in which you have a table which is generated using a linear equation and you merely want to reproduce the linear equation.Select any two distinct points, each of which will be represented by an ordered pair.
Suppose the pairs are (p, q) and (r, s).
Then the gradient of the line is (q - s)/(p - r).
Then using the point-and-gradient form of the equation:
y - s = [(q - s)/(p - r)]*(x - r)
Then simplify and rearrange to the required form.
The second case is where the table is based on observations for two variables which are linearly related. However, due to random variations or measurement errors (or rounding), the scatter plot for the data is nearly - but not quite a straight line. You will then need to use statistical techniques to obtain the equation. The best known is the method of least squares. However, this site does not support the mathematical symbols to illustrate the procedure.
What three things make a linear equation special from other equations?
it is a straight line
the slope is extremely easy to pick out
it always passed the vertical line test
Three examples of system of linear equation?
1.
x + 2y = 5
3x + 6y = 10
2.
x + y + z = 50
2x + 5y = 8z = 4
6x + 7y + 9z = 7
3.
x + 2y = 5
1.2x + y = 10
How do you apply linear algebra to economics?
The application of linear algebra to economics lies primarily in its use of matrices. A matrix in economics is used as a means to solve a large number of linear equations at once, where the variables are economic indicators and factors. As a whole, then, a matrix represents a transformation from one state to another state, and one can view the economy as a succession of such states. The methods can be extended to linear combinations of non-linear equations, where the entries might be operators rather than numbers. Given the huge number of factors involved, linear algebra has various methods for reducing the complexity of the problem. It also investigates properties of matrices such that one need not always waste time trying to find the precise solutions in order to determine some property of the system. Simulations of systems often use matrices.
What is the Jacobi iteration scheme for a system of linear equations?
Jacobi iteration is used to diagonalize a matrix or system of equations, by applying well-chosen rotations. These rotations are chosen to zero particular off-diagonal elements. It might be guessed that the process would only need to be done once for each off-diagonal element, but in fact each iteration destroys some of the zeros created during previous iterations. Nevertheless, the process does converge to a diagonal system.
Can linear equations have fractions as constants?
Yes. A fraction is still a number after all.
Application: say you have y=(1/2)x+6, the slope is 1/2 so you start at 6 on the y-axis and go up one and over 2 and you have your next point (x=1). It's the same thing as saying the value of x is being divided by 2. If you can multiply x by a number, why can't you divide?
a more complex one would be y=(3/4)x+9 in which case, you're both multiplying and dividing. You're multiplying x by 3 and dividing that by 4.
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". Please use "brackets" (or parentheses).
For example, here it is not clear whether you mean
3/4*x + 10
or 3/4*(x+10)
or 3/(4x) + 10
or 3/(4x + 10)
An additional source of confusion is that none of these give 12 as an answer.
What property of inequality would you use to solve the equation 14x equals 35?
None. Properties of inequalities are not that relevant when solving equalities.
