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Abstract Algebra

Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.

1,849 Questions

How do you write a C-program for matrix multiplication?

it would have a part in it like this:

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

. for (j=0; j<l; ++j) {

. . sum= 0;

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

. . . sum += a[i][k] * b[k][j];

. . }

. . c[i][j] = sum;

. }

}

How do you cheat on online tests for algebra II?

I don't know what kind of test it is. If it only ask for answers, you can use tools like Wolfram, Mathematica to figure the answer out for you. You gain absolutely nothing useful though.

What is the value of a 1958 quarter?

If the coin shows any wear at all, the value is for the silver about $3.50 the coin is a very common high mintage year.

What is the slope of the line that passes through the points 9 5 and 7 10?

For (x,y) coordinate sets: (9,5) and (7,10) Slope is rise over run = (delta Y / delta X) = [ (10-5) / (7-9) ] = (5/ -2) = - 5 / 2 Or when reduced, it will be negative 2 and one half.

When do you capitalize algebra?

When the word is at the start of a sentence.

How do i get dotted lines in ireport?

click on it, then in properties, under graphic properties, change the pen...

hope it helps. {I'm using iReport 5.1.0}

1957 dime value?

6-4-11>>> Unless it is a proof or very high-grade uncirculated coin the value is mostly for the silver, about $2.60. All silver Roosevelt dimes (1946 to 1964) are considered common.

What is the value of an eddy stone rifle?

I paid $200 to a friend for a 30-06 in used but working order. Origins of it are unknown. (I am using a friends computer)

How many cenimeters are in a gram?

centimeters measure length. grams measure weight. the two are not interchangable

What does S R followed by a number mean?

If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.

What is the value of a 1919 penny?

1919 Wheat Penny: With no mint mark, in good condition is worth $0.15, uncirculated is worth $20.00. With D mint mark, in good condition is worth $0.25, uncirculated is worth $80.00. With S mint mark, in good condition is worth $0.15, uncirculated is worth $70.00. 1919 is not a rare date for Lincoln cents. In average circulated condition, its value is about 5 cents. Retail is 20 cents in ANA Good condition. Up to $50 if it is uncirculated and has a D mintmark.

What is the value of 1986 Krugerrand?

Its value is based only on the gold it contains -- currently about $600 per ounce.

What is the value of a 1964 Remington 870 gun?

i paid 150 for an 870 express used in exelent shape 4 years ago, but that was a real good deal.

Can electric field intensity be a scalar quantity?

No,because electric field (force/charge) is a vector quantity, i.e. , it has both magnitude as well as direction.

What are the applications of linear transformations?

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.

Is there exist a matrix whose eigenvalues are different that of its transpose?

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.

How To Do Algebra?

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.

What is the value of an 1971 Kennedy 12 dollar?

Kennedy Half dollars are very common, coins from 1971 to date contain no silver and are only face value.

What is the value of a Browning 12 gauge?

In order to answer your question,you will need to provide the serial number to age your shotgun.The overall condition including the amount of original finish on the metal and wood,and the bore condition to give a accurate value to your shotgun.All these factors come into play when evaluating the shotgun for price.

What is the value of a 22 LR Chicopee Falls R920 patented April 17 1994?

That patent date would be in 1894, not 1994. You have a version of the Stevens 'Favorite' boys rifle. Can be collectable in excellent condition and/or rare variations, but the more common variants in typical condition rarely exceed $200. sales@countrygunsmith.net

How do you algebra?

In algebra, there will be letters. Each letter represents a number. Different letters stand for different numbers.

e.g. x=1 but y=3. if there are many X's, they all mean the same thing.If there is a number before the letter, you multiply the number by what the letter represents.

So 3p means 3*p. This is very simple algebra.

I haven't learned complex algebra yet, but i can understand it. But can't explain it well.

Why is algebra efficient?

Consider it first as a set of instructions to perform 1 or more arithmetical operations on any related values:

V = IR means multiply I by R to find V whatever the values for I and R.

(This is Ohms' Law if the letters stand for Voltage, Current and Resistance in a simple electrical circuit!)

Consider next that you can alter the order and signs by definite rules:

If V = IR then R = V/I and I = V/R.

So we can abbreviate the operations, rather like a knitting-pattern or chess notation - AND we can manipulate the original equation to suit the particular task.

So at once, even for a simple, practical use like that, we have an efficient, elegant way to express what we need to do to perform the task.