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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 two linear functions?

y = 0 and y = 1 are two linear functions. They're not especially interesting ones.

What are eigenvalues and eigenvectors?

An eigenvector is a vector which, when transformed by a given matrix, is merely multiplied by a scalar constant; its direction isn't changed. An eigenvalue, in this context, is the factor by which the eigenvector is multiplied when transformed.

Which are linear system and non linear system?

Linear system has a proportional slope, which gives the system a straight line. And, a non-linear system has a non-proportional slope, which is represented by a non-straight line (usually a curved one). Feel free to edit if you think this is not to the point.

Do Venus fly traps live in the desert?

No venous fly traps do not live in the dessert they live in mostly the rain forest or some place were it rains a lot.

What kind of equation is BaC2 H2So4BaSo4 2HC?

An impossible one.

Barium Carbide (BaC) does not exist.

2HC should be H2C2, acetylene.

There is no such element as So. If you want the sulphate ion (or sulfate), the O needs to be in capitals.

How is graphing a linear inequality different than graphing a linear equation?

In an inequality, you have to shade a side of a line to see show if the possible answers are greater than or equal to it

How are linear equations used in business?

liner equations can b used in business for getting the rough estimate of the profit or loss using a variable in the place of a quantity which is unknown.

How do you generate a parity check matrix?

In order to generate the parity check matrix you must first have the generator matrix and the codeword to check and see if it is correct.

1. Place your generator in row reduction form

2. Get the basis vectors

3. Put the vectors together to get the parity check matrix

4. Check it b multiplying the codewords by the parity = 0

For an example: 2*4 Generator Matrix

[1 0 1 1

0 1 1 0]

Rank = 2...therefore the number of columns is 2...Rank + X = # of columns of the Generator matrix

v1+v3+v4 = 0

v2+v3 = 0

v1 = -r1-r2

v2 = -r1

v3 = r1

v4 = r2

Parity = [-1 -1

-1 0

1 0

0 1]

How do you use different techniques to solve linear equations?

1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.

2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.


3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.

What is the gcf of 36 48 48?

factor all three then use the prime numbers that are in all three.

36=2x2x3x3

48=2x2x2x2x3

2x2x3=12 the gcf

Is the equation 4y2x linear?

Without an equality sign it is not an equation but an expression

What do you mean by the term linear?

Linear means that the largest power(index) in the expression, equation, inequality etc, =1

What is the most expensive college in the US?

Here are the top 5 universities on Forbes' list:

Sarah Lawrence College - $57,556

Bronxville, New York

Columbia University - $54,385

New York, New York

Bard College - $54,275

Annandale-on-Hudson, New York

Wesleyan University - $53,976

Middletown, Connecticut

Vanderbilt University - $53,660

Nashville, Tennesse

What is the difference between tensors and matrices?

A scalar, which is a tensor of rank 0, is just a number, e.g. 6

A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3]

A matrix, which is a tensor of rank 2, is a group of vectors, e.g.

1 6 3

9 4 2

0 1 3

A tensor of rank 3 would be a group of matrix and would look like a 3d matrix.

A tensor is the general term for all of these, and the generalization into high dimensions.

What is the Celsius intercept?

It depends on in what context: Kelvin or the archaic Fahrenheit measure.

How do you write a C-program for matrix multiplication?

it would have a part in it like this:

for (i=0; i<n; ++i) {

. for (j=0; j<l; ++j) {

. . sum= 0;

. . for (k=0; k<m; ++k) {

. . . sum += a[i][k] * b[k][j];

. . }

. . c[i][j] = sum;

. }

}

How do you cheat on online tests for algebra II?

I don't know what kind of test it is. If it only ask for answers, you can use tools like Wolfram, Mathematica to figure the answer out for you. You gain absolutely nothing useful though.

How do i get dotted lines in ireport?

click on it, then in properties, under graphic properties, change the pen...

hope it helps. {I'm using iReport 5.1.0}