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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.

500 Questions

What is non-examples of empire?

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Asked by Wiki User

A banana is a good non-example. Even a banana republic is not likely to be confused with an empire!

What is the answer to 12x-30 equals 114?

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Asked by Wiki User

12x-30=114

12x=114+30

x=144 / 12

therefore x=12

What is the word equation for BaCl2 Na2SO4?

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Asked by Wiki User

barium chloride plus sodium sulphate yields barium sulphate plus sodium chloride

What are your two numbers if their sum is -5 and their product is 4?

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Asked by Wiki User

Let the number be 'm' & 'n'

Hence

Sum = m + n = -5

Product = mn = 4

Algebraically rearrange the product to m = 4/n

Substitute into the Sum

(4/n) + n = -5

Multiply through by 'n'

Hence

4 + n^2 = -5n

n^2 + 5n + 4 = 0

It is not in Quadrtatic form . to solve.

Hence

(n - 1)(n - 4) = 0

n = -1 & n = -4

Are the two numbers.

What is 3x4t?

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Asked by Wiki User

The answer is 12t.

Is this statement true or false A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line?

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Asked by Wiki User

The statement "A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line" is true.

What is an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line?

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Asked by Maddieford

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line (-7,3); x=4

What is The square root of x-10 equals x-2?

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Asked by Wiki User

To find the solution to the equation √(x-10) = x-2, we can square both sides. This gives us x-10 = (x-2)^2. Expanding the right side gives x-10 = x^2 - 4x + 4. Rearranging the terms and simplifying, we have x^2 - 5x - 6 = 0. By factoring or using the quadratic formula, we can determine the solution(s) to the equation.

How do you write exponents in WORD?

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Asked by Wiki User

To write exponents in Microsoft Word, you can use the superscript feature. Simply select the number or letter you want to raise to an exponent, go to the "Home" tab, and click on the "Superscript" button (usually represented by a small "x^2" icon). This will format the selected text as a superscript, indicating it is an exponent.

How are linear equations similar or different from functions?

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Asked by Wiki User

A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.

What is 7.82 plus 31.23?

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Asked by Wiki User

7.82 plus 31.23 is equal to 39.05.

What are small red dot like spiders that are found in large numbers?

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Asked by Wiki User

Let's see, if these spiders are around plants, my guess is that they are spider mites. Damage from these little guys can be severe. Leaves turn silver, as the chlorophyll disappears, or turn yellow as they die. Leaves fall on the floor for no apperant reason. A slight red dust can be found on the underside of leaves. I have never dealt with this problem, I bet a nusery worker would know how to get rid of them. Rinsing your plants every now and then can detour many pests and diseases.

Worlds most expensive college?

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Asked by Wiki User

Technical university In russia. It costs 83,125 thousand U.S dollars.

What is a radical equation?

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Asked by Wiki User

They are actually to the one half power. You can take a factor in the radical and sqrt it and put in on the outside...

Ex.

sqrt(28) = sqrt(4 * 7) = sqrt(22 * 7) = 2sqrt(7)

sqrt(28) = 2 * sqrt(7)

What are the practical applications of logarithms in the field of engineering science business and economics?

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Asked by Wiki User

Logarithms were originally used to convert multiplications into additions and divisions into subtractions (plus some looking up in tables).

To multiply 3456 by 6789

  1. Look up in table: log(3456) = 3.5386
  2. Look up in table: log(6789) = 3.8318
  3. add them together = 7.3704
  4. Look up in table: antilog(7.3704) = 107.3704 = 23460000

So the only calculation is a simple addition at step 3.

Logarithms were often used for approximate calculations (4 significant figures), but there were tables for more accurate work.

Nowadays, though, it is easier to use calculators for multiplication and division.

There is a whole class of problems where the solution involves logarithms. If the rate of change in a variable X is directly proportional to the quantity X, then the solution involves logarithms (or its inverse, exponents). Typical textbook examples include radioactive decay, simple chemical reactions, bacterial {or any uncontrolled] growth, compound interest.

How is tin used in everyday life?

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Asked by Wiki User

Tin is used to coat metals to prevent corrosion (tin cans are made from tin coated steel).

Tin is also an alloying agent. Important tin alloys such as soft solder, type metal, fusible metal, pewter, bronze, bell metal, babbitt metal, white metal, die casting alloy, and phosphor bronze.

The Pilkington Process is used for producing glass; this involves floating molten glass on molten tin to produce a flat surface.

Tin salts are sprayed onto glass to produce electrically conductive coatings. These salt treated panes can be used for panel lighting and for frost-free windshields.

Some magnets are made of crystalline tin-niobium wire, which is super conductive at low temperatures. These magnets weigh just a few pounds; yet produce magnetic fields comparable to those of 100-ton electromagnets.

How do you write a c program to read two numbers and perform addition and subtraction of two matrices?

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Asked by Wiki User

#include<stdio.h>

#include<conio.h>

void main()

{

clrscr();

int a,b,c,n;

printf("enter the numbers");

scanf("%D",&n);

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

a=b;

a=c;

c=a+b;

printf("the sum is %c",);

getch();

}

What is the output variable of a function?

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Asked by Wiki User

It is a value in the co-domain [range] of the function.

What types of math are used in chemical engineering?

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Asked by Wiki User

Chemical engineers use Optimization Techniques and Operations Research to optimize and bring out the most suitable design with appropriate parameters.

Chemical engineers use Computational Fluid Dynamics involving lots of complex calculus to solve complicated fluid system and heat transfer problems.

Chemical engineers fit data for accurate graphical analysis using methods of regression and other graph techniques.

Chemical engineers use Partial Differential Equations and Ordinary Differential Equations using either manually or by Polymath, Matlab, Wolfram Mathematica to solve and get a solution to system of equations.

Chemical engineers use Numerical Analysis and techniques to solve a variety of problems based on the dynamic nature of the system.

Chemical engineers use Surface Volume, Area, 3-D geometry and vector algebra for material analysis and assessing physical parameters to plant systems and units.

What are fundamental units?

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Asked by Wiki User

Fundamental unitsFundamental units, or base units, are those that cannot be decomposed into more basic units. (Note that "basic" does not mean "smaller.") Derived units, on the other hand, are those that are defined in terms of other units, which may be base units or other derived units.

In the SI system, the base unit of length is the meter, the base unit of mass is the kilogram, and the base unit of time is the second. The base unit of electrical current is the ampere which is defined in terms of the force between parallel, current-carrying conductors.

One of a set of unrelated units of measurement, which are arbitrarily defined and from which other units are derived. For example, in the SI system the fundamental units are the meter, kilogram, and second.

Write a program to obtain transpose of a 4 X 4 Matrix in c using functions?

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Asked by Wiki User

void main()

{

int arr[4][4];

int i,j,a,b,f;

printf("\nInput numbers to 4*4 matrix");

for(i=0;i<4;i++)

{

for(j=0;j<4;j++)

{

printf("\nKey in the [%d][%d]) value",i+1,j+1);

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

}

}

for(i=0;i<4;i++)

{

for(j=0,f=0;j<4;j++)

{

if(i!=j&&f==0)

continue;

a=arr[i][j];

b=arr[j][i];

arr[i][j]=b;

arr[j][i]=a;

f=1;

}

}

for(i=0;i<4;i++)

{

for(j=0;j<4;j++)

printf("%d ",arr[j][i]);

printf("\n");

}

}

What are the main areas of maths used in mechanical engineering?

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Asked by Wiki User

Everything in engineering requires applications of mathematics.

Is this a joke? Mathematics is the QUEEN of the sciences. she RULES engineering. Without math, you have no engineering, any kind of engineering. Think of Mathematics as the Venus of the sciences.

How do you write a C program for a matrix multiplication using array?

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Asked by Wiki User

include <stdio.h>

int main()

{

int m, n, p, q, c, d, k, sum = 0;

int first[10][10], second[10][10], multiply[10][10];

printf("Enter the number of rows and columns of first matrix\n");

scanf("%d%d", &m, &n);

printf("Enter the elements of first matrix\n");

for ( c = 0 ; c < m ; c++ )

for ( d = 0 ; d < n ; d++ )

scanf("%d", &first[c][d]);

printf("Enter the number of rows and columns of second matrix\n");

scanf("%d%d", &p, &q);

if ( n != p )

printf("Matrices with entered orders can't be multiplied with each other.\n");

else

{

printf("Enter the elements of second matrix\n");

for ( c = 0 ; c < p ; c++ )

for ( d = 0 ; d < q ; d++ )

scanf("%d", &second[c][d]);

for ( c = 0 ; c < m ; c++ )

{

for ( d = 0 ; d < q ; d++ )

{

for ( k = 0 ; k < p ; k++ )

{

sum = sum + first[c][k]*second[k][d];

}

multiply[c][d] = sum;

sum = 0;

}

}

printf("Product of entered matrices:-\n");

for ( c = 0 ; c < m ; c++ )

{

for ( d = 0 ; d < q ; d++ )

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

printf("\n");

}

}

return 0;

}

What math used in Mechanical Engineering?

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Asked by Wiki User

First off, the question should be either "What math is used in Mechanical Engineering? or What is the highest level of math someone needs to take in order to become a Mechanical Engineer?"

Most college programs require through Differential Equations to earn a BS degree in ME. This means you would need to take Calculus 1, 2, and 3, Linear Algebra, and Differential Equations once you get to college. It is assumed that most students going into engineering will have no less than Pre-Calculus before entering college while most will have taken Calculus. Now each college has different requirements for fulfilling the math requirements for an engineering program. I know from my experience, Georgia Tech teaches math differently than most colleges because they combine Calc 1-3 and Linear Algebra into just 3 courses instead of 4.

My suggestion is look at the program requirements at the school you are interested in first. Second, evaluate whether you feel that you can learn the math. For those who struggle with math, if you really want to be an engineer, I suggest going to a smaller school where the class size will be smaller. This will have better student/teacher interaction so you can get more help.