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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 are some equivalents to 5 radical 3?
5 radical 3 is just a number.
So, asking this is the same as asking 'What are some equivalents to 3?' One could answer 2 * 3 / 2. But this reduces to 3.
The situation is the same for your question. One could offer some multiple of 5 radical 3 as an answer but, being a multiple, it would reduce to 5 radical 3.
radical 3 is approximately 1.732 but not exactly 1.732 so one cannot say, for instance, that 5 radical 3 = 5 (1.732) = 8.660. In fact, there is not way of expressing radical 3 with a finite number of decimal places. So no-one can write radical 3 = 1.732.... exactly.
5 radical 3 is the best one can do.
What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
What are the 5 steps solving the mathematics?
There aren't. There are many problems in mathematics that have yet to be solved. If there were only five steps, they would all have been solved by now! So, obviously, there must be more than 5 steps.
What symbol will you find in every linear equation?
The equals sign ( = ).
In fact it defines any equation, linear or not, since an equation is a statement that a particular value or term is equal to, so the result of solving, a second set of terms and operators.
Any other symbols would be particular to the equation you have derived or are trying to solve.
What is the solution to this equation negative 2x plus 14 equals 0?
2x + 14 = 0
Subtract 14 from each side of the equation: 2x = -14
Divide both sides of the equation by 2: x = -7
You can also obtain solutions to equations by visting wolframalpha.com. Enter solve 2x+14=0, for example. You can click on the 'step-by-step' button to see how the equation was solved.
An arithmetic sequence does not have a constant rate of increase or decrease between successive terms, so it cannot be called anything!
The constant increase or decrease is called the common difference.
rise refers to the y coordinates(i.e y2 - y1) whereas the "run" refers to the x coordinates(i.e x2 - x1), hence the algebraic expression slope = rise/run or to put it mathematically, m = (y2 - y1)/(x2 - x1) or m = change in y/change in x.
If the figures in the table are exact and without measurement error then take any two of the points (x1, y1) and (x2, y2) and use these to form the linear relation
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
If, however, you suspect that the values in the table do not exactly follow a linear relationship then use linear regression for which formulae are provided in wikipedia.
What is linear momentum of a system of particles?
The linear momentum of a system of particles is simply the vector sum of the linear momentum of each of the particles.
What is dependent and inconsistent system?
Suppose we have two linear equations in two unknowns. If the equations are plotted on a rectangular grid, the graph will fit one of these scenarios:
1) The two lines cross each other (intersect).
2) The two lines don't cross - they are parallel lines
3) The two lines fall on top of each other - they're really the same line.
In case 3) the two lines are dependent - one can be changed into the other. In cases 1) and 2) we say the lines are independent.
If the pair of equations has a solution (one or more points in common) we say they are consistent ... cases 1) and 3). In case 2) the system is inconsistent; there is no solution.
To summarize:
1) Intersecting lines are consistent and independent.
2) Parallel lines are inconsistent and independent.
3) Coincident ["happen together"] lines are consistent and dependent.
*** A second order linear system CANNOT be both dependent and inconsistent.
Symmetrical bilateral transfer is the learning or relearning of skills for an individual. Symmetrical bilateral transfer occurs when an individual has traumatic brain injuries or autism spectrum disorders.
What is a linear equation that is not true for even one real number and therefor has no solution?
A linear equation in one variable.
Case 1: A conditional equation: True only for a value of the variable.
Ex.
x + 2 = 3, True only when x is 1.
Case 2: Identity Equation: Always true.
Ex.
x + 2 = x + 2, True for any value of x.
Case 3:
x + 1 = x + 5, False for any value of x.
We call a solution any value of the variable that satisfies the equation, meaning if we replace the variable with that value, the equation becomes a true statement.
Example:
-2(x -3) = 8 - 2x
-2x + 6 = 8 - 2x (add 2x and subtract 6 to both sides)
0 = 2 False. Since this equation, which is equivalent to the original equation, is false, then the original equation is also false. Meaning, there is no real number for x that could satisfy the equation. So there is no solution to the equation.
What absolute value inequality has 6 and -10 as two of its solutions?
There are many possible answers but the simplest is
|x + 2| = 8
Which of the following systems of equations has no solution?
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
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 find the point two lines intercept at given the slopes and Y-intercepts of both lines?
Solve the two equations simultaneously. The solution will be the coordinates of the point of intersection.
What is called Substitution method?
When you have a system of equations and you can solve for one in terms of th others and then replace it in the other equations that is substitution.
x+y=15
x-y=1
well the second one can be x=1+y
x+y=15 then can be (1+y)+y=15 by substitution.
1+2y=15
2y=14
y=7
Then x+7=15
x=8
What is a unique solution in linear equations?
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.
What is the advantages or disadvantages of solving system of non-linear equation?
The main advantage is that many situations cannot be adequately modelled by a system of linear equations.
The disadvantage is that the system can often get very difficult to solve.
How is the law of reflection used in everyday life?
When people look in your mirror to shave, apply make-up, etc.
