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Does Cramers rule apply to systems of 4 equations with 4 variable or higher?
Wiki User
∙ 13y ago
Yes, but the matrices get fairly complicated.
Example:
aW + bX + cY + dZ = e
fW + gX + hY + iZ = j
kW + lX + mY + nZ = o
pW + qX + rY + sZ = t
|a b c d| | W | | e |
|f g h j| | X | | j |
|k l m n| | Y | = | o |
|p q r s| | Z | | t |
Solving for W is not easy...
|e b c d|
|j g h j|
|o l m n|
|t q r s|
----------
|a b c d|
|f g h j|
|k l m n|
|p q r s|
Wiki User
∙ 13y ago
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Can the same variable equal two different numbers in one equation?
No, but a variable can have more than one value in an inequality such as x > 10. In that inequality, x can be 11, 12, 13, 14, or anything else higher than 10.That is not to say, however, that the same variable can't be equal to two different expressions or formulas. The equations x=10 and x=y+5 are completely valid. In fact, those expressions imply that 10=y+5, or that y=5.
Would you say that systems that have higher efficiency rations than other systems will always have higher utilization ratios than those other systems?
This is not always true. Other systems may be utilized more than this faster system for other reasons not listed here.
What does it mean when a positive correlation coefficient between the dependent variable Y and the independent variable X indicates?
It means that the two variables are likely dependent. The higher the number of the positive correlation the stronger the connection.
What two variables does a scatter plot have?
independant-influences the other variable-x axis dependant-is influenced by the dependant variable-y axis example as johnny jumps from a higher distance, he falls faster. independant=distance from the ground dependant=the speed of the fall
What is a positive negative correlation?
Correlation determines relationship between two variables. For example changes in one variable influence another variable, we can say that there is a correlation between the two variables. For example, we can say that there exists a correlation between the number of hours spent on reading and preparation and the scores obtained in the examination. One can infer that higher the amount of time spent on preparation may result in better performance in examination leading to higher scores. Hence the above is a case of positive correlation. If an increase in independent variable leads to an increase in dependent variable, it is a case of positive correlation. On the other hand if an increase in independent variable leads to a reduction in dependent variable, it is a case of negative correlation. An example for negative correlation could be the relationship between the age advancement and resistance to diseases. As age advances, resistance to disease reduces.
How can you tell if a graph is a linear function?
The word linear means in a straight line. If the graph is a line, it is linear. Also, linear equations are of the first order; they contain a variable but not a square (or higher power) of a variable. If the equation contains x2 it is not linear.
What is differential equations as it relates to algebra?
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
Is COGS a variable cost?
COGS is a mixed bag of fixed and variable costs. Overall, however, it generally behaves like a variable cost; in general, the more units that are produced, the higher inventory production costs will be, and the higher inventory production costs are, the higher COGS will be.
What correllation is discovered when higher scores on one variable is associated with lower scores on another variable?
A negative correlation
What relationship do quadratics and polynomials have?
In algebra polynomials are the equations which can have any number of higher power. Quadratic equations are a type of Polynomials having 2 as the highest power.
What calculators solve linear equations?
The Texas Instument TI-84 model or higher
How do you create an equation for a parabola?
An equation for a parabola always has some type of irregular variable, usually a squared variable or higher.
Is a variable annuity a good 403B investment?
Fees are higher in a Variable annuity than they are in say a fixed Index Annuity.
What has the author Avron Douglis written?
Avron Douglis has written: 'Ideas in mathematics' -- subject(s): Mathematics 'Dirichlet's problem for linear elliptic partial differential equations of second and higher order' -- subject(s): Differential equations, Linear, Differential equations, Partial, Dirichlet series, Linear Differential equations, Partial Differential equations
What is a local variable and What statements are able to access a local variable?
A local variable is a variable that can only be called on by the module. Where as a global variable can be called upon by any module. Only statements made inside the same module can call on a local variable.
What best describes the notion that the higher the level of ones education the higher ones income level will be?
independent variable
Will you earn a higher interest rate with a variable annuity than with a fixed annuity?
Yes, you do earn a higher interest rate with a variable annuity than with a fixed annuity. It depends on what kind of interest rate you have at the moment.
