Linear Algebra

There are infinite varieties of dimensions as 4'x6' , 3'x8', 12'x2', ..., etc

No, a Kilogram (Kg) is not an independent variable. An independent variable is any system that remains free from change If something else changes.

We would therefore say a Kilogram is a dependent variable. The amount of Kilograms depends on the amount of fat, water, organs, etc stored.

Some students have trouble with word problems. They may not fully understand what the question is asking. They may not understand topic. Or they might not be the smartest in word problems. If so , I would consider a tutor.

1

360

These are square numbers of 3, 4, 5 with alternating sign, I'd expect to continue the sequence with

36, -49, 64, -81, 100

Suppose you had a secret message you needed to give someone. You can use a matrix to make it unreadable to anyone except the recipient.

First, you must have an encoding matrix. Let's suppose your encoding matrix is...

-2 2 3

-1 3 2

2 1 3

And your message is... I like matrices

You must then write you message with numbers.

Suppose you use the code A=1, B=2, C=3 etc. Spaces are 27.

That would make your message this:

9 27 12 9 11 5 27 13 1 20 18 9 3 5 19

You translate this into a matrix, going down the columns. The matrix must have three rows to be able to multiply.

9 9 27 20 3

27 11 13 18 5

12 5 1 9 19

When you multiply the two, you get...

72 19 -25 23 61

96 34 14 52 50

81 44 70 85 68

To find the original message, you multiply by the inverse

of the encoding matrix--the decoding matrix. You will find the first pattern of numbers and be able to find the message.

(Sorry, I don't know how to make matrix brackets. You'll just have to deal with it. I tried to make it pretty clear.)

if you are talking about regular polygons, then nothing has an obtuse angle. otherwise, pretty much any shape can have an obtuse angle

if you are good at math, you would know. I'm not being mean, but sometimes it takes a little help from an adult.

Suppose you have the points with coordinates (p, q) and (r, s)

then, provided p is different from r,

the slope of the line is (q - s)/(p - r) = m, say.

Then, if (x, y) is any point on the line,

(x - s)/(y - r) = m

That, after simplification, is the linear equation of the line.

This will be a lot simpler when you have numerical values for p, q, r and s rather than work algebraically throughout.

If p is not different from r, then the equation is x = p (or r), a vertical line.

I have the job you may be looking at and once you get the job it is just basic math

Try using this website (see related links below).

ex. y= 2x+3

The slope is how the line slopes so this one would be 2 or on the graph, up 2 and right 1.

The y-intercept is where the line crosses the y-axiz or (0,3).

So plot (0,3) and go up 2 right 1 for about 3 points and if you need more you can reverse the direction and go down 2 left 1.

Whatever isn't 5(x - 1)(2x + 3)

2y-4x=-12 Add 4x to each side

2y=4x-12 Divide each side by 2

y=2x-6 The y-intercept is (0,-6)

Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions.

4x + 3y = 4

x - 2y = -10, so add 2y to both sides gives x=2y-10, replace this into first equation gives:

4(2y-10) + 3y = 4, expand that gives 8y-40+3y=4, add 40 to both sides, this gives:

8y + 3y =44, or 11y = 44 giving you y=4.

You have solved for y, now solve for x:

4x + 3y = 4, gives 4x +12 = 4, or 4x=-8 giving x=-2.

So x=-2 and y=4.

QED.

To be a linear equation, the equation must be set equal to Y. Also, it can't have any square roots, or any variables on the bottom of a fraction.

In general, the terms of a linear equation must be either first-degree polynomials with respect to the variables, constants, or products of the two. This disallows terms involving trigonometric, logarithmic, exponential, hyperbolic, and power expressions (except for the power of 1) and their inverses.

A line segment is a line with two points. When drawn, there are no arrows coming out of the points.

Matrices are used in pretty much any situation where several linear equations are involved. They're used all over the place in physics, chemistry, engineering, and economics. I linked a site below with more information.

Yes. You can obviously have a set of lines with no common intersection, can't you?

they are oin the newer versions since 2007 of books:alg1,2 and geometry so far what i know and you ususlly find them at the end of a lesson at the bottom of the page, or you are able to watch videos on the codes in the middle of the page that say wideo tutor

Call your matrix A, the eigenvalues are defined as the numbers e for which a nonzero vector v exists such that Av = ev. This is equivalent to requiring (A-eI)v=0 to have a non zero solution v, where I is the identity matrix of the same dimensions as A. A matrix A-eI with this property is called singular and has a zero determinant. The determinant of A-eI is a polynomial in e, which has the eigenvalues of A as roots. Often setting this polynomial to zero and solving for e is the easiest way to compute the eigenvalues of A.

None. The data set has no elements and so there cannot be any central tendency.