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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
How do statisticians use algebra?
One example is linear transformations, which are a key element of statistics. The fact that a linear transform of a Normal variabe is also a normal variable is central to the use of z-scores for calculating normal probabilities and so for hypothesis testing.
How can graphs be used to estimate the solution for a system of linear equations?
Graphs can be used in the following way to estimate the solution of a system of liner equations. After you graph however many equations you have, the point of intersection will be your solution. However, reading the exact solution on a graph may be tricky, so that's why other methods (substitution and elimination) are preferred.
Under what condition is the product of skew-symmetric matrices skew-symmetric?
I could be wrong but I do not believe that it is possible other than for the null matrix.
How do you find the equation of the axis of symmetry of y equals 2x plus 2 plus 4x plus 2?
y = 2x + 2 + 4x+ 2 = 6x + 4
This is NOT a symmetric function and so there is no axis of symmetry.
How do solve for the variable over a number in a linear equation?
Well a variable in a number in a linear equation is basically the variable divided by a number. So if you have x over 10, it is basically x times 1/10. You can solve by having either another equation and use either point slope or y=mx+b.
Is it possible that there will be no feasible solutions in linear programming?
Yes. Although possible in real life, it is unlikely in school examples!
How many hours will take when traveling at 80 kilometers per hour to cover 77 kilometers?
Just use the basic formula for speed: distance = speed x time. Solving for time: time = distance / speed.
How do you separate Hydrogen and Oxygen gases in industrial electrolysis of water process?
In electrolysis, oxygen and hydrogen gas are produced at different electrodes (oxygen at the anode and hydrogen at the cathode). Since these electrodes do not have to be in close proximity, the hydrogen and oxygen will bubble upwards into separate collection vessels.
If you needed to separate hydrogen and oxygen once mixed, the easiest way I can think of would be to cool the mixture to ~60K. At this point the oxygen would condense and leave hydrogen gas.
Algorithm for transpose of matrix?
transpose(Matrix mat,int rows, int cols ){ //construction step Matrix tmat; for(int i=0;i<rows;i++){ for(int j=0;j<cols;j++){ tmat[j][i] = mat[i][j]; } } }
What is a word equation and a formula equation?
A word equation is where you describe a reaction using the chemicals by their names
Eg. Hydrogen+Oxygen>Water
A formula/symbol equation is where you use each chemical's formula (which is a group of the elements it consists of)
Eg. H2+O2>H2O (you should use small letters for the numbers after the element)
When you call adjacency matrix in symmetric matrix?
If your graph is undirected, then its adjacency matrix will be symmetric.
Faizan
System of linear equation in one unknown?
A system of linear equations that has one unknown is a set of equations that all depend on the same variable. An example is y = 1 + 3x and y = 4 + 7x.
A vector space is an algebraic structure with two binary operations, + and *, that satisfy the following axioms:
1) Associativity: a + ( b + c ) = ( a + b ) + c
2) Commutativity: a + b = b + a
3) Addition identity: a + 0 = a
4) Additive inverse: a + a-1 = 0
5) Scalar distributivity with respect to vector addition: c*(a + b) = c*a + c*b
6) Scalar distributivity with respect to field addition: (c + d)*a = c*a + d*a
7) Compatibility: c*(d*a) = (c*d)*a
8) Scalar multiplicative identity: 1*a = a
For the above axioms a, b, 0, Є Vand 1, c, d Є F where V is a set of vectors over the field F. Most of the time F = R or C, which are the sets of real and complex numbers, respectively.
Dot and cross product between 3D and 4D?
here are the possible answers:
A) A tridimensional vector
B) A 4D vector
C) A 5D vector
D) An scalar number
E) It is undefined
How can you find the independent variable for x in 2x -4y equals 8?
2x - 4y = 8
2x = 4y + 8
x = 2y + 4
What is the best website to learn algebra 2 on the Internet for free?
Khan Academy. Khan Academy covers almost everything in the world.
What are two linear functions?
y = 0 and y = 1 are two linear functions. They're not especially interesting ones.
