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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
Many people use Algebra, like doctors, builders, archetecs. Many people with good jobs use Algebra so that's why its is very important to learn Algebra. You truly use it in the future when you grow up.
Algebraists use algebra.
What is the formula to get the full name of the data in columns E,F,G row 23?
Algebra is used all the time. Many equations can be created for many things, and it's all thanks to algebra. Physics, Engineering, Computers, and most other technical professions require algebra, as well as higher mathematics. For someone who plans not going into the technical professions, basic things such as balancing your checkbook, and dealing with taxes often require atleast some knowledge of algebra.
What is the definition of solution of system of linear equations?
The values for which the equations are solved.
Graphically the intersection of the lines that are the solutions to the individual equations. The link below gives some explanations. The equations themselves will have to be given for a solution to be found.
A = coefficient matrix (n x n)
B = constant matrix (n x 1)
How do you solve compound interest formula for n?
It depends on which compound interest formula you mean. Refer to the Wikipedia Article on "Compound Interest" for the correct terminology.
x - 2y = -6
x - 2y = 2 subtract the 2nd equation from the 1st equation
0 = -8 false
Therefore, the system of the equations has no solution.
It is called solving by elimination.
What is a variable that may influence the dependent variable other than the independent variable?
experimental variable?
Is the sum of two linear functions always a linear function?
Yes. You would have to multiply to change it.
What does it mean when a linear equation does not have a slope?
You get a straight line. as in 2x + y.
* * * * *
Wrong!
2x + y is not a line, it is an expression.
The standard form of the equation of a line is y = mx + c where m is the slope.
If there is no slope, then m = 0 and so the equation becomes y = c. This is a straight line parallel to the x-axis.
Can we transform columns in gauss elimination method?
yes it is possible.not only columns but also rows can be transformed.
How do you graph the system of linear inequalities?
Graphing an inequality such as y > mx + b is similar to graphing the equation y = mx + b, with a couple of differences:
- Since it is not equal, you draw a dashed line, rather than a solid line.
- If y is greater than: shade the area above the dashed line; less than: shade below the dashed line.
Since it's a system of linear inequalities, you will wind up with different shaded areas which overlap, creating a bounded area.
These types of problems usually come from some sort of real-world situation, such as finding optimum products from limited resources. Example is a farmer has a fixed number of acres to plant (or can use for cattle grazing, instead). Some crops grow faster than others, so time in-season is a limiting factor. Other things, such as money (how much to be spent on seed, watering, fertilizer, people or equipment to harvest, etc.)
The areas which overlap represent the scenarios which are possible with the given resources. Then you can look at the graph and figure out where there is a maximum profit for example.
Both are same..just the names are different.
What is the disadvantage of substitution of systems of equations?
If done properly there are no disadvantages.
What is an extraneous solution to the equation x-3 equals sq rt 5-x?
x - 3 = √(5 - x); square both sides, for the left side use (a - b)2 = a2 - 2ab + b2
x2 - 6x + 9 = 5 - x; add x and subtract 5 to both sides
x2 - 5x + 4 = 0; this is factorable since 4 = (-1)(-4) and (-1) + (-4) = -5
(x - 1)(x - 4) = 0; let each factor equal to zero
x - 1 = 0; x = 1
x - 4 = 0; x = 4
Check if 1 and 4 are solutions to the original equation.
1 - 3 =? √(5 - 1)
-2 =? √4 (recall the radical symbol is looking only for the positive root)
-2 = 2 false, so that 1 does not satisfy the original equation, so it is an extraneous solution.
4 - 3 =? √(5 - 4)
1 =? √1
1 = 1 true, so that 4 is a solution to x - 3 = √(5 - x).
Can you Give an example of bounded function which is not Riemann integrable?
Yes. A well-known example is the function defined as:
f(x) =
* 1, if x is rational
* 0, if x is irrational
Since this function has infinitely many discontinuities in any interval (it is discontinuous in any point), it doesn't fulfill the conditions for a Riemann-integrable function. Please note that this function IS Lebesgue-integrable. Its Lebesgue-integral over the interval [0, 1], or in fact over any finite interval, is zero.
