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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 best estimate of 512 25?
The best estimate is the true value.512 = 2^9 = 2^7*2^2 = 128*4
Then 512*25 = (128*4)*25 = 128*(4*25) = 128*100 = 12800.
When should you use a multiplication to solve a system of linear equestions by elimination?
When the coefficients of the variables in the linear equations are different.
If
eqn(A): ax + by+ cz + ... = m, and
eqn(B): px + qy + rz + ... = n
where x, y z are variables and the rest are constants, then
p*eqn(A) = pax + pby+ pcz + ... = pm and
a*eqn(B) = apx + aqy + arz + ... = an
The coefficients of x, pa and ap, are equal and so subtracting one equation from the other will eliminate x.
How do you know that a table value is a linear function?
There are several ways to do that. For example, you can actually graph the function. Or, you can check the ratio of the differences between the points. If this ratio (change in y, divided by change in x) is constant, the function is linear.
What is the classification of a system of equations?
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
How we solve equations of motion by graph?
One can solve equations of motion by graph by taking readings of the point of interception.
How did you graph a linear equation in two variables?
By using the formula for a straight line equation graphed on the Cartesian plane by means of the x and y axes.
Steps of how to solve a system of equations by substitution?
Step one is by expressing one of the equation into one term that is taking one unknown in the form of other. Step two is replacing the unknown into equation 2. Step 3 is replacing the found unknown into one of initial equations to find the other unknown.
How do you graph using the rate of change and initial value?
Normally on the Cartesian plane using as for example the straight line equation y = mx+c whereas m is the gradient or slope and c is the y intercept.
What are lines that have equivalent linear equations and overlap at every point when graphed?
coincidental -Lines that share the same solution sets.
What is the chromatic polynomial of Peterson graph?
The chromatic polynomial for the Petersen (not Peterson) graph is
pi(z) = (z - 2)* (z - 1)*z*(z^7 - 12*z^6 + 67*z^5 - 230*z^4 + 529*z^3 - 814*z^2 + 775*z - 352).
What is the equation of a line that is perpendicular to and passes through the point (4 6)?
That would depend on its slope which has not been given.
The slope of a linear function is also a measure of how fast the function is increasing or decreasing. The only difference is that the slope of a straight line remains the same throughout the domain of the line.
What does the slope of a linear function indicate?
- In the graph, the slope means that, what is the corresponding value of f while x vary, for example, f(x)=2x+3, when x=1, then f=5 etc
What are the following points on the line given by the equation y 2x?
As Anand said, the question is vague. However, two important points for any equation are the x and y intercepts. For y = 2x, the x-intercept is (0,0) and the y-intercept is (0,0). Not sure if that helps.
What is a proportional relationship between 2 quantities?
A [directly] proportional relationship between two variables, X and Y implies thatY = cX where c is the constant of proportionality.
What is the slope for y equals negative two over three x plus two?
If: y = -2/3x+2 then the slope is -2/3 and the y intercept is 2
Is it possible to have a system of linear inequalities where solution is every point in the entire?
Yes, you can say something like y < infinity and y > -infinity .
How do I write a system of linear inequalities?
Instead of using y = mx + b you use y (inequality sign) mx + b. By inequality sign, I mean symbols like <,>
How do you know if an equation is linear?
You know if an equation is linear if it is a straight line. You can also know if the equation is y = mx + b where there are no absolute values nor exponents.
The quotient works out as: x^2+2x+4 and there is a remainder of -3
Let x be the smallest number to be solved:
- x + (x+1) + (x+2) = 123
- 3x + 3 = 123
- 3x = 123 - 3 = 120
- x = 120 / 3 = 40 is the smallest number
- and 40 + 41 + 42 = 123
