Linear Algebra

the reason some parts of the earth are more prone to having earthquakes is because of the fault line the cities are built on.

To graph a linear equation, one must first simplify it into the slope-intercept form, y=mx+b, where m is equal to the slope of the line. Next, one must find the x and y coordinates. By making x equal to zero the equation can be simplified into y=b, giving the coordinate (0,b). Plot this point on your graph. By making y equal to zero, the equation becomes x=[(-b)/m], giving the coordinate ([(-b)/m], 0). Plot this point on your graph. Once you have both coordinates marked, simply connect these two points with a line.

the substitution method in which you take each variable and you find out the value and then plug it into the original equation.the adding and subtracting method in which you subtract\add equations to take out a variable and you can figure out what the other variable is. then you also substitute that into that into the original variable

That's the way it is defined.

It means that one of them depends on the other. When you change one, the other usually changes in some way.

Many relations are functions like y=3x2 - x + 7. Other relations, such as x2 + y2 = 25, are not functions, but they are still relations.

Blue probably

6 + 9 = 10x

6n + 9n = 10

6 (x + 9) = 10x - 18

Remember variable's power will be never more than one.

4

1m = 100cm, therefore 12m = 1200cm. 12m is > 120 cm

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

Linear transformations can be very important in graphics. Also, linear transformations come up whenever you need to solve systems of linear equations, which arise quite often. Finally, they can be useful in further areas of mathematics such as topology.

zero is the answer

yea!

No. Say your matrix is called A, then a number e is an eigenvalue of A exactly when A-eI is singular, where I is the identity matrix of the same dimensions as A. A-eI is singular exactly when (A-eI)T is singular, but (A-eI)T=AT-(eI)T =AT-eI. Therefore we can conclude that e is an eigenvalue of A exactly when it is an eigenvalue of AT.

It is really a fun!

What is the number next to 12? 13 is the answer. Ok. Next to 25? 26 is the right answer. Now next to 102? 103 is the correct one.

Now seriously, what is next to a? Usually almost all of us would say it is b. But it is absolutely wrong!

Then what will be right answer?

Let us analyse what we have done in the previous cases? We have added 1 to get the next number. Right? So next to a has to be a+1 and not b. This is algebra. Instead numbers, we use alphabets too to do mathematical manipulations. So a+b is a+b. No chance of adding as we add 2+6 as 8. Because a may assume any value. It may be 9, -3, ./2 , 3/4 , 0.78 or any value. Same away b may assume any value.

Now a+a? Instead simply writing as a+a we can simplify writing as 2a. Hence 4m+3m = 7m and so on.

Then a multiplied by b will be written as a*b or simply as ab. So abcd will be the product of a, b, c and d.

If a is multiplied by a then AA may be marked. It may give an inconvenience if we multiply a's some four times. Instead writing aaaa, it will be easier and convenient to write as a4. This is how algebra grows in an interesting way. Then we come across many identities such as (a+b)2=a2 + b2 + 2ab.

The dot product can be used as a half space test. A half space test can be used to determine if an object, lets say a zombie, is in front of the player (or camera) or behind it. If my player's forward vector is P and the vector from the player to the zombie (zombie's position - player's position) is Z, then dotting P and Z would give me the angle between the two vectors. If the angle is positive our player is facing the zombie, otherwise the zombie is behind us (never turn your back on a zombie!).

If your equation is in the form ax2 + bx + c, it can always be solved for x by using the quadratic formula.

x = -b plus or minus the square root of (b2 - 4ac) with the whole thing divided by 2a

Let's try an easy example: x2 + 3x - 4 = 0

That's factorable: (x + 4)(x - 1) so we already know what the answers are (-4, 1)

Now let's plug in the quadratic formula where a = 1, b = 3, c = -4

x = -3 plus or minus the square root of (3)2 -(4)1(-4) divided by 2(1)

Simplified, that's -3 plus or minus the square root of 25 divided by 2

Our two answers are (-3 + 5) divided by 2 and (-3 - 5) divided by 2

2/2 = 1 and -8/2 = -4

Non-factorable equations work just as well, except the answer won't be a whole number. It'll be some nasty decimal or an imaginary number.

In the context of geometry, related to a line.

In an algebraic context, an equation or expression where each of the unknown variables appears with a power of 1. If there are n variables, then such an equation, plotted in n-dimensional coordinate space would be a straight line.

All equations for which the greatest power of its variable is 1, and that have no absolute value signs surrounding the variable, is linear. Therefore, yes, your problem is linear.

In dry air at sea level and atmospheric pressure, 1.69 seconds.

The first 9 is in the Millions place, the second is in the Hundreds. The difference is 4 orders of magnitude.

Matrices are a vital mathematical tool for calculating forces, vectors, tensions, masses, loads and a myriad of other factors that must be accounted for in engineering to ensure a safe and resource-efficient structure.

The relevant domain is the set of values that the variable in question can take. Some variables, such as age or length, for example, cannot be negative; some variables, such as the number of children in a class must be whole numbers.