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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
What is the slope intercept form when a vertical line is passing through 5 -8?
The slope of a vertical line is undefined and so there cannot be a slope-intercept form of the equation.
How do you get the value of 100 using number 1 five times?
111-11=100..
This way, you used the number 1 five times and reached the value of a 100.
Let x = pounds of $0.75 candy, and let y = pounds of $1.25 candy.
From the question, we know the total pounds must equal 9, and the total price should be 9 pounds at $0.96 per pound. Thus the total price should be 9*0.96 = $8.64.
We can form two equations; one for total pounds, and one for total price:
x+y = 9
0.75x+1.25y = 8.64
Solve for x in the first equation: x = 9-y
Plug that into the second equation for x: 0.75(9-y) +1.25y = 8.64
Simplify: 6.75 - 0.75y + 1.25y = 8.64
More: 6.75 + 0.5y = 8.64
More: 0.5y = 1.89
Divide both sides by 0.5: y = 3.78
Plug that into the first equation: x + 3.78 = 9
Solve for x: x = 5.22
Thus, we need 5.22 pounds of $0.75 candy and 3.78 pounds of $1.25 candy
How many millaliters is 300 marbles?
None, since there is no such thing as a millaliter.
Furthermore, marbles come in all sorts of sizes.
How do you solve algebra of sets?
There is quite a lot of algebra devoted to solving problems involving sets, parts of sets, and concepts closely related to sets, such as subsets, cosets, and groups. You'll need to be more specific.
How many scores in 10 decades?
A score is 20 years. A decade is 10 years. So in 10 decades we've had 100 years. Thus there are 5 scores in 10 decades.
10 Years/1 Decade x 10 Decades ÷ 20 years/1 score = 5 scores
Can you multiply a 2x2 matrices?
You can definitely multiply 2x2 matrices with each other. In fact you can multiply a AxB matrix with a BxC matrix, where A, B, and C are natural numbers. That is, the number of columns of the first matrix must equal the number of rows of the second matrix--we call this "inner dimensions must match."
Is the standard reciprocal function bounded?
No.
As you approach zero from the left, the value increases without bound. As you approach zero from the right, the value decreases without bound.
Yes that is correct
What group of numbers does pi belong to?
Pi is both an irrational number and a transcendental number.
What are examples of periodic matrix?
A square matrix X is periodic if Xn = I, the identity matrix, and its period is n.
If n = 1 then trivially, X = I, and Xk = I for all k.
However, if n > 1, then Xn = I but Xk is not I for any k < n.
Then Xna+b = Xna*Xb = Ia*Xb = Xb for all a. That is, X has a period of n.
It can be shown that X, X2, ... , Xn-1 and I are distinct matrices that form a Group
What is 0 3 and a slope of negative one-fourth look like in slope intercept form?
Assuming that one fourth is your way of spelling one fourth, the equation is: y = 0.25x + 3
or 4y = x + 12
How do you put 5.42x10-4 in standard notation?
It is: 5.42*10-4 = 0.000542 by moving the decimal point 4 places to the left
What two numbers can you multiply to get -24?
Assume we want to determine the integers that multiply to obtain -24.
Here are the possible pairs:
- -1 and 24
- 1 and 24
- 2 and -12
- -2 and 12
- 3 and -8
- -3 and 8
- 4 and -6
- 6 and -4
What is the boolean expression for a 2 out of 3 OR gate?
If the inputs are ABC. The inputs required to give an output are ABC, AB, AC and BC. Using the Absorption law X + X.Y = X we can remove ABC, the inputs required are therefore AB, AC and BC.
What is law of vector addition?
Let x = [x1, x2, ... xk] and y= [y1, y2, ... yk] be the two vectors of length k.
Then we define their sum to be x+y = [x1+y1, x2+y2, ... xk+yk]
In other words, add the corresponding elements in the two vectors.
What does position to term rule mean in maths?
In the study of sequences, given a number n, the position to term rule tells you how the nth term of the sequence is calculated.
