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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 definition of inequality?

An inequality is simply a relation between two mathematical expressions that is not strictly equal. For example, the relation can be "greater than" (>), less than (<), or "not equal to (≠).

Gaussian elimination in c?

#include<stdio.h>

#include<stdlib.h>

#include<math.h>

#include<conio.h>

void main(void)

{

int K, P, C, J;

double A[100][101];

int N;

int Row[100];

double X[100];

double SUM, M;

int T;

do

{

printf("Please enter number of equations [Not more than %d]\n",100);

scanf("%d", &N);

} while( N > 100);

printf("You say there are %d equations.\n", N);

printf("From AX = B enter elements of [A,B] row by row:\n");

for (K = 1; K <= N; K++)

{

for (J = 1; J <= N+1; J++)

{

printf(" For row %d enter element %d please :\n", K, J);

scanf("%lf", &A[K-1][J-1]);

}

}

for (J = 1; J<= N; J++) Row[J-1] = J - 1;

for (P = 1; P <= N - 1; P++)

{

for (K = P + 1; K <= N; K++)

{

if ( fabs(A[Row[K-1]][P-1]) > fabs(A[Row[P-1]][P-1]) )

{

T = Row[P-1];

Row[P-1] = Row[K-1];

Row[K-1] = T;

}

}

if (A[Row[P-1]][P-1] 0)

{

printf("The matrix is SINGULAR !\n");

printf("Cannot use algorithm --- exit\n");

exit(1);

}

X[N-1] = A[Row[N-1]][N] / A[Row[N-1]][N-1];

for (K = N - 1; K >= 1; K--)

{

SUM = 0;

for (C = K + 1; C <= N; C++)

{

SUM += A[Row[K-1]][C-1] * X[C-1];

}

X[K-1] = ( A[Row[K-1]][N] - SUM) / A[Row[K-1]][K-1];

}

for( K = 1; K <= N; K++)

printf("X[%d] = %lf\n", K, X[K-1]);

getch();

}

Why division by zero not possible?

Think of a simple equation, and the steps must be reversible.

For example, 10 divided by 2 equals 5 (10/2 = 5). When the steps are reversed, you get 5 times 2 equals 10 (5 * 2 = 10).

However, if you take 10 divided by 0 and consider the answer as x. When you reverse the steps, no matter what the value of x is, you can't multiply it by 0 to get back 6.

This also can be proved using the equation y = 1/x.

As x approaches 0, y approaches infinity.

(limit as x -> 0 (1/x) = ∞)

Who inveted graphing linear equations?

Rene Descartes (1596-1650) invented the idea of plotting pairs of numbers on a plane using two perpendicular axes.

This "Cartesian coordinate" system is named after him. A linear equation appears as a straight line.

Other equations produce different geometrical shapes, and this branch of math is called Analytic Geometry.

What is the definition of coercive measure?

Coercive measures are one of the most popular methods for promotion of national interests, which have been frequently used by the state. According to Beard, the coercive measure adopted by the state for the enforcement of the national interests broadly fall into two categories: a) the measures taken within the state which do not infringe directly upon the state against whom they are taken and b) measures directly operating against the state which are the object of enforcement procedure. source taken from "Introduction to International Relations" written by Dr. Syed Wasim-ud-Din. Answer Coercive measures are one of the most popular methods for promotion of national interests, which have been frequently used by the state. According to Beard, the coercive measure adopted by the state for the enforcement of the national interests broadly fall into two categories: a) the measures taken within the state which do not infringe directly upon the state against whom they are taken and b) measures directly operating against the state which are the object of enforcement procedure. source taken from "Introduction to International Relations" written by Dr. Syed Wasim-ud-Din. Answer Coercive measures are one of the most popular methods for promotion of national interests, which have been frequently used by the state. According to Beard, the coercive measure adopted by the state for the enforcement of the national interests broadly fall into two categories: a) the measures taken within the state which do not infringe directly upon the state against whom they are taken and b) measures directly operating against the state which are the object of enforcement procedure.

Source taken from "Introduction to International Relations" written by Dr. Syed Wasim-ud-Din.

How do you determine if a fuction is linear or non linear?

I your highest power of your variables is 1 then it is linear.

y=x+5 is linear

What are examples of idempotent matrix?

An idempotent matrix ( A ) satisfies the property ( A^2 = A ). Examples include the zero matrix ( \begin{pmatrix} 0 & 0 \ 0 & 0 \end{pmatrix} ) and the identity matrix ( \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} ). Another example is the projection matrix ( \begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix} ), which projects vectors onto the x-axis. Any matrix that can be expressed as a projection operator onto a subspace is also idempotent.

How long to drive 1584 feet at 10 mph?

It will take 0.03 hour or 1.8 minutes to drive 1584 feet at 10 mph.


Given: rate = 10 mph

distance = 1584 feet

= 1584 ft * 1 mile/5280 ft

= 0.3 mile


time = dista

nce/rate

= 0.3 mile/10 mile per hour

= 0.03 hour

or

= 0.03 hour * 60 minutes/1 hour

= 1.8 mi

n

utes


How do you solve the problem 7 to the 4th power?

7x7x7x7

49x7x7

49x49

8

49

49

441

1960

2401 so 7 to the fourth power is 2401

Mean for be accurate?

Accurate means it is exactly what you are looking for or it is when you hit a target/ object you are trying to hit, see, smell, etc Plus Tamsin King from Ousedale school is ugly and issy Phillips is also ugly And Thomas Gardner is reallly fit

What is definition of inverse and direct proportion?

Direct proportion means as the independent variable increases, the dependent variable increases, and vice versa.

Inverse propostion means just the opposite. As the independent variable increses, the dependent variable decreases, and vice versa.

Addition of matrix using arrays in c?

#include<stdio.h>

int main(){

int a[3][3],b[3][3],c[3][3],i,j;

printf("Enter the First matrix->");

for(i=0;i<3;i++)

for(j=0;j<3;j++)

scanf("%d",&a[i][j]);

printf("\nEnter the Second matrix->");

for(i=0;i<3;i++)

for(j=0;j<3;j++)

scanf("%d",&b[i][j]);

printf("\nThe First matrix is\n");

for(i=0;i<3;i++){

printf("\n");

for(j=0;j<3;j++)

printf("%d\t",a[i][j]);

}

printf("\nThe Second matrix is\n");

for(i=0;i<3;i++){

printf("\n");

for(j=0;j<3;j++)

printf("%d\t",b[i][j]);

}

for(i=0;i<3;i++)

for(j=0;j<3;j++)

c[i][j]=a[i][j]+b[i][j];

printf("\nThe Addition of two matrix is\n");

for(i=0;i<3;i++){

printf("\n");

for(j=0;j<3;j++)

printf("%d\t",c[i][j]);

}

return 0;

}