Linear Algebra

The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A

The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A

01

The word "billion" as used in English-speaking countries means 109 (a one, followed by 9 zeros). Therefore, to convert this to standard form, you simply move the decimal point 9 positions to the right - filling out with zeros as needed.

It is a negative multiple of x.

It is a negative multiple of x.

It is a negative multiple of x.

It is a negative multiple of x.

Input and output tables are used to organize data for various purposes. Common types include truth tables in logic that display the relationship between inputs and outputs for logical expressions, and function tables that show how different input values produce specific outputs in mathematical functions. Additionally, data tables in databases organize records with defined fields for efficient data retrieval and analysis. These tables help visualize relationships and facilitate decision-making across various fields.

There was a time when this rule was considered a wonderful piece of magic, called the "rule of three"; students just learned to do it without expecting to understand why it worked. That makes me sad! With algebra, it's almost obvious, and certainly not something special. I'll try to express this in a way that students who don't know algebra (or don't realize how much of it they have already seen) can follow. Remember that if you have two equal quantities and multiply them by the same amount, the products will again be equal. So if we multiply the fractions a/b and c/d by b, the results are equal: a c --- * b = --- * b b d which can be written as bc a = ---- d Now we can multiply both fractions by d: bc ad = ---- * d d which, of course, means ad = bc I personally prefer not to cross multiply, but just to multiply by whichever denominator helps. In your example, 3/15 = n/30, I would just multiply both sides by 30 and get n = 30*3/15 = 30/15*3 = 2*3 = 6.

I would like to add that cross products are used to find the unknown of a proportion (or ratio) that already exists by the nature of the equality.

For example a recipe calls for 2 cups of flour to make 4 pancakes but I want 12.

I can say 2 is to 4 what x is to 12 and set up the ratio:

2/4 :: x/12

2 x 12 = 4x (cross multiply)

24 = 4x

24/4 = x (and divide)

x = 6 cups of flour

this method is also used (transparently) in chemistry and engineering, and is crucial in solving algebraic equations.

12,1212

No. The speed sensor is located on the transmission, and is what drives the speedometer cable, which drives the speedo head. The speedo head is another name for the the speedometer, which is the display gauge that you see while sitting in the car.

The area of a square is 16 cm2 What are the linear dimensions

The slope is 3.

In the case I would first write ALL factors of 600 and find the differences.

1x600

2x300

3x200

4x150

5x120

6x100

8x75

10x60

12x50

15x40

20x30

24x25

The one that subtracts to give the answer is -20 and 30

#include<iostream>

#include<stdio.h>

#include<conio.h>

using namespace std;

int main()

{

int a[20][20],b[20][20],c[20][20],i,j,k,m,n,f;

cout << "Input row and column of A matrix \n\n";

cin >> n >> m;

cout << "\n\nInput A - matrix \n\n";

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

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

cin >> a[i][j];

cout << "\n\nMatrix A : \n\n";

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

{

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

cout << a[i][j] << " ";

cout << "\n\n";

}

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

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

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

cout << "\n\nTranspose of matrix A is : \n\n";

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

{

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

cout << b[i][j] << " ";

cout << "\n\n";

}

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

{

for(j=0;j<m;j++){

c[i][j]=0;

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

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

}

}

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

{

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

{

if((int)c[i][i]==1&&(int)c[i][j]==0)

f=1;

}

}

cout<<"\n\n Matrix A * transpose of A \n\n";

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

{

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

cout << c[i][j];

cout << "\n\n";

}

if(f==1)

cout << "\n\nMatrix A is Orthogonal !!!";

else

cout << "\n\nMatrix A is NOT Orthogonal !!!";

getch();

return 0;

}

-ALOK

18

• corners of most buildings
• sides of picture frames
• sides of rectangular windows
• corners of kitchen refrigerators and stoves

#include<

5*3y+1+12y-1 = 15y+1+12y-1 = 27y.

3 and 91 multiplied together make 273

All that matters once you have y = -2x is the y-intercept.

Examples:

y = -2x +3

y = -2x - 8

y = -2x + 4

You can change the y-intercept to whatever numbers you want.

One extra hint: All the lines with the slope of -2x will be parallel on a graph, no matter what the y-intercept is.

When you are dealing with a number of variables and relations between them.

6x plus 3y minus 2x plus 5y equals 4x plus 8y.

If we are talking about the algebraic expressions, then an expression can be simplified or be evaluated for specific values of its variables, while an equation need to be solved, in other words to find the values of the variables that make the equation a true statement.

If we are solving an equation, then we can work in the same way that we can simplify an expression (since an equation is a statement that states that two expressions are equal), or factoring an expression.

Since it has no equal sign, this isn't an equation. I believe you have to spell it out as "equals" in your question, due to restrictions imposed by Answers.com.

A tridiagonal matrix is one in which the only non-zero elements are on the principal diagonal, and the two diagonals immediately next to it: one below and the other above.