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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 the applications of linear transformation in engineering?
There are four forms of linear transformation on the Cartesian plane which is used in engineering and they are:-
Translation moves a shape in the same direction and distance
Refection is a 'mirror image' of a shape
Enlargement changes the size of a shape by a scale factor
Rotation turns a shape through an angle at a fixed point
When is there one solution to a system of linear equations?
When the solution is equal to a number, in other words, only one solution happens if you solve for your variables. 0 = 0 means there are many solutions and a number not equal to another number has no solution.
How do you solve systems of equations using linear combination?
You select the linear combination of the equations in such a way that at each stage you eliminate one variable.
You select the linear combination of the equations in such a way that at each stage you eliminate one variable.
You select the linear combination of the equations in such a way that at each stage you eliminate one variable.
You select the linear combination of the equations in such a way that at each stage you eliminate one variable.
Escalation matrices are used as a hierarchy system in case of major issues. They contain multiple user contacts that can be contacted in a certain order should something go wrong with parameters, such as time zone, schedule, partner, and customer.
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.
You will obtain a more accurate answer than is possible using graphical methods. It's faster and less work than using a table.
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.
Is the point 39 a solution of the equation y8x-9?
The expression of y8x-9 has no solution because without an equality sign it can not be considered to be an equation.
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.
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.
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
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
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.
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
