Linear Algebra

Since n! is the product of all the numbers from 1 through n and (n+1)! is everything in n! multiplied by n+1, the quotient is n+1 ■

In computer based applications, matrices play a vital role in the projection of three dimensional image into a two dimensional screen, creating the realistic seeming motions.

Stochastic matrices and Eigen vector solvers are used in the page rank algorithms which are used in the ranking of web pages in Google search.

The matrix calculus is used in the generalization of analytical notions like exponentials and derivatives to their higher dimensions.

One of the most important usages of matrices in computer side applications are encryption of message codes.

Matrices and their inverse matrices are used for a programmer for coding or encrypting a message.

A message is made as a sequence of numbers in a binary format for communication and it follows code theory for solving.

Hence with the help of matrices, those equations are solved.

With these encryptions only, internet functions are working and even banks could work with transmission of sensitive and private data's.

32 - 121 - 64 = 36x => -153 = 36x so that x = -4.25

perfect square of 16= 4 because 4 times 4 is 16.

Yes, a system can, in fact, have exactly two solutions.

It can be a ray if it does not include the end point or a half line if it includes the end point.

77 and 86 degrees, respectively.

The answer depends on what form the equation is in and what form you want it in. The standard form is ax + by +c = 0 where x and y are variables and a, b and c are constants.

There are also the 1-d equivalent: ax + b = 0

and 3-d equivalent: ax + by + cz + d = 0

and, equivalent equations in spaces with higher dimensions.

If you mean: 6x = 25+x then x = 5

negativeand positive

Usually yes.

You plug in a number for "x" and then solve for "y". Do it 3 times and if they are on the same line it should be correct.

They are the same.

It is a function from the set of x-values to the set of y-values.

15;hours

distance=velocity X time

so,if time decreases distance also decreases.

If we think in a general way,if we have more time,we can travel more distance.

If we have less time,then we'll be able to travel less distance/

The area in the inequality gives you choices. Like the number of pounds that an elevator can carry is anything less than its maximum.

1. Data collection through interview, source documents and personal observation.

2. Defining the problem in deatil.

3. Setting the system objective.

4. Establishing constraints.

5. Determining information needs and sources.

6. Develop alternative designs and select the best.

7. Documenting the conceptual design.

8. Detailed system analysis

No because irrational numbers can not be expressed as fractions whereas rational numbers can be expressed as fractions

False. There can either be zero, one, or infinite solutions to a system of two linear equations.

(x - y)2 - z2 is a difference of two squares (DOTS), those of (x-y) and z.

So the factorisation is [(x - y) + z]*[(x - y) - z]

= (x - y + z)*(x - y - z)

Press the button "global" and you will see 1B Transpose +00. Use the 'yes' and 'no' to go up or down by semitones. If you don't see 1B after pressing 'Global',scroll till you find it using the up and down buttons

Yes

No. A scalar matrix is a diagonal matrix whose main diagonal elements are the same. Only if the diagonal elements are all 1 is it an identity matrix.

Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist.

If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,.

If the dimension of the solution space > 0, then there are infinitely many solutions.