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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 three ways of solving system of linear eqution?
Systems:
1. Solve for a letter and substitute into the other equation. It is called substitution.
2. Linear combination. Set the equations so the letters match up. Multiply one of the equations so one of the letters will go to zero when yoy add them together and solve for the other letter.
3. Determinants. Setting up square matrix and substituting into the matrix to find the different variables.
When you use cross product and dot product in vector?
Dot product and cross product are used in many cases in physics. Here are some examples:
- Work is sometimes defined as force times distance. However, if the force is not applied in the direction of the movement, the dot product should be used. Note that here - as well as in other cases where the dot product is used - the product is greatest when the angle is zero; also, the result is a scalar, not a vector.
- The cross product is used to define torque (distance from the axis of rotation, times force). In this case, the product is greatest when the two vectors are at right angles. Also - as in any cross product - the result is also a vector.
- Several interactions between electricity and magnetism are defined as cross products.
Is the input in a function table supposed to be the same as the rest of the input?
No, because then the output would be the same as the rest of the output(s).
Is negative numbers counting number?
If you mean, "Can you use negative numbers arithmetically?" then yes.
E.g. 6 + 8 = 14
6 + (-8) = 6-8 = -2.
Why would you look at a logarithmic chart instead of charting the absolute values of the variables?
Whether you should look at logarithmic charts or absolute values depends entirely on the nature of the variables.
How can the degree of the equation tell us if the equation is linear or not?
A linear equation always has a degree of one because the slope has to be constant to form a line. So, x + 7 is linear, 7 - x is linear, 4x - 3.7 is linear, but anything with x2 , etc. is not linear.
What is the equation of a line that has a slope of 2 and passes through negative five and one?
It is: y = 2x+11
Algebraic Properties of Matrix Operations. In this page, we give some general results about the three operations: addition, multiplication.
What do you have to remember when you add linear functions?
Rearrange both equations into like form, by this I mean like variable should line up AND the equal marks must line up.
Add LIKE Terms only straight down keeping the equal marks in the same place.
EX
2x - 3y = 7
4x +3y = 5 Add like terms
6x = 12 ( y terms 'cancel' because there opposites)
This is usually the whole purpose, to make one variable cancel.
I made this up so that the 'y' variables would cancel. If they won't then you must find their LCM and multiply whole equations to cause them to cancel.
Ex: x + 3y = 7
2x + 5y = 12 ---- if you want 'y' to cancel 3 and 5 have a LCM of 15
make one of them become -15
5(x + 3y = 7)
-3(2x + 5y = 12)
5x + 15 y = 35
-6x - 15 y = -36 ----- now add
-1x = -1
How is exponential equation used today?
It is used in the same way that it was in the past!
It is relevant for compound growth (for example, interest on investment or simple population growth) or compound decrease (depreciation or radioactive decay). There are also very many other situations where the change in a variable is directly proportional to the value of the variable.
How do I solve 8x minus 5 equals 2x plus 5?
8x - 5 = 2x + 5
Add 5 to both sides: 8x = 2x + 10
Subtract 2x from both sides: 6x = 10
Divide both sides by 6: x = 10/6 = 5/3 or 1.66... recurring.
What is the greatest 1.414 or 1.2?
1.414 is. the 4 is bigger than the 2. that is why. Go from left to right. if one number is bigger than the other then you have found the larger
What is the determinant of the matrix 241142335?
Assuming the matrix is a 3x3 matrix of 1-digit number, it is 23. Otherwise it depends on how the 9 digits split up.
Nothing does cubiods and cubiods do nothing. Apart from all that, there is no such thing as a cubiod!
Why is linear equations called linear equations?
Because its linear and the equation is a problem to solve
How can one establish Richardson - Dushmann equation?
http://www.lepp.cornell.edu/~ib38/uspas05/set3.pdf
