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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

What is the mathematical meaning of range?

The range of a data set is the difference between the last and greater value subtract..

Example:

9,8,7,6,5,4

Since 9 is bigger and the 4 is the smallest

subtract 9 and 4 = answer

How are addition and multiplication used to solve a linear equation?

The multiplication is used to solve a liniar equation is when you have for example x/5=10 when you have a number divided by another number you need to multiply both sides with the denominator of x to get the number. In this case the answer is 50. Lets check

50/5=10

10=10 yes its right

Addition is used to answer a linear equation when you have for example this equation:

x-5=20

To get the answer you need to add the opposite o the number adding/subtracing x. In this example it is -5. So when you add the opposite you need to add 5 this will end up with

x=25 lets check

25-5=20. yes its correct

now lets use all the learning so far.

to start lets start with an equation.

x/2-5=10

first we will need to add 5

x/2=15

second we need to divide/multiply

x=30

third you need to check

30/2-5=10

15-5=10

10=10 yes its correct

Is y-7 plus 6x a linear equation?

Without an equality sign it can't be considered to be an equation

How do you solve -4x - 5x 9?

Assuming that's -4x - 5x + 9, the answer would be x =1
As -4x - 5x + 9 = 0
Making it 9 = 5x + 4x, or 9 = 9x, cancel out the 9's, making x = 1.

If it's -4x - 5 x 9, the answer would x = 11.25
As -4x - 5 x 9 = 0
Making it 45 = 4x, divide the 45/4, which would give you 11.25.

What is newton-raphson formula for finding roots of non linear equations?

The Newton-Raphson method works if the equations are differentiable over the domain.

Let f(x) be the non-linear equation and f'(x) by its derivative [with respect to x].

Start with a reasonable guess at the answer, x0.

Then calculate the sequence xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, …

The N-R method should converge to a root.

What is the solution of 6x-2y equals 22?

6x - 2y = 22

Solve for x:

6x = 2y + 22

x = 1/3y + 11/3

Solve for y:

-2y = -6x + 22

y = 3x - 11

You can not simplify the equations further without having one of the variables solved, or having more than 1 equation (such as a system)

What is subtistution in mathematical terms?

It is using a set of two equations, adding them together, eliminating one variable and finding the value of the other variable.

Convert a canonical form to linear form?

plz sir tell me how to convert the canonical form into stanadard form in boolean expression.We have this prblem in digital logic design

What is the matrix's in oder?

Restate the question: "What is the order of a matrix?"

The order of a matrix tells the number of rows and columns in the matrix. For instance, a matrix with 3 rows and 4 columns is a 3x4 matrix ("three by four").

A square matrix has the same number of rows and columns: 2x2

What is a product. What is Product Personality and its components?

A product is a physical good that is marketed usually for a profit. A product's personality is it's usability, performance, appearance, and benefits.

What is the advantage that the method od substitution has over the graphing method of solving system of equations?

Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).

What is addition?

Addition [3+47]

Addition is a way of combining 2 numbers.

For example:

I have two apples and Joe gave me 2 more..I now have 4 apples if I count all of them up!

Why is the rate of chage 0?

I assume you are asking about using differentiation. In this case, where dy-by-dx=0, there is a stationary point on the graph i.e. where the gradient is equal to 0.

Why is it that the students failed in Mathematics?

The most common reason is because when the student go home he/she doesn't continue there studies there.

Solve linear equations with complex coefficients on both sides?

You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.