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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 -9 is less than or equal to 4x plus 3 is less than or equal to 11?
-9 < 4x + 3 < 11
Subtract 3 from each expression: -12 < 4x < 8
Divide each term by 4: -3 < x < 2
How matrix are different from scalar?
A scalar is any single number, like 27, while a matrix contains at least 2 numbers such as [27, 3].
How many two digit numbers are there in which the sum of the digits is greater than their product?
24 two digit number, which sum is greter than their product.
Which are following:
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91
Why is wind considered a vector field?
At each point in space, the wind has a velocity, which is a vector. Another way of saying the same thing is that at each point, the wind blows at a certain speed and in a certain direction.
What does it mean to evalutate the expression?
Replace each variable in the expression by its value and then find the value of the expression.
What are some real life applications of abstract algebra?
By definition, none. For if it did have real life applications it would not be called abstract!
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You could consider it as establishing the rules by which the algebra needed to perform real-life tasks works.
For a simple example, if C = AB then you could say, "Fine, suppose we call A and B the sides of rectangle than C is its area, OR if we call A and B speed and time respectively then C is the distance travelled.
In both cases the algebraic rules are the same: multiply two values and you obtain their product; but many practical applications are in fact simple products so there we have the underlying pure algebra for solving them. And from that we can use pure algebra rules to determine A or B from the others.
Why in computer or in any other digital circuit design the help of boolean algebra is used?
Boolean algebra is used in logic circuits. Using And, Nor, Xor and Nand gates to determine the state of an output, dependant on the condition of various inputs.
Or, if you like, to make a fixed decision based on the inputs.
When designing a logic circuit, it is easy to get confused by too many steps in the process to get the answer that you want.
By using Boolean algebra, the steps can be rationalised and reduce to the minimum number of steps, before committing to a finished physical circuit.
What country does algebra comes?
The first comprehensive book on algebraic methods was published by the Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, in Baghdad. However, algebraic methods were used for centuries before that in various countries.
What is a number sentence using 3 and 6 and 18?
im on this problem, only got 3, wayyy to hard! sorry. i got 3times6= 18 18/6=3 6*3=18
How can you prepare for algebra 1?
I have taken Algebra I and made an 99 easily. You must learn to memorize how to solve equations and various formulas. Be prepared to right out long equations and use substitution and elimination to simplify equations. Also, pay attention in class.
What is the physical interpretation of gradient of a scalar field and directional derivative?
The elevation of points on a hill is a scalar 'field'. It can have a different value
at every point, but each one is a scalar value.
Imagine a lumpy bumpy irregular hill, and pick a point to talk about, say,
somewhere on the side of the hill.
At that point, the directional derivative of the elevation is the rate at which
the elevation changes leaving the point in that direction.
It has different values in different directions: If you're looking up the hill, then
the d.d. is positive in that direction; if you're looking down the hill, the d.d. is
negative in that direction. If you're looking along the side of the hill, the d.d.
could be zero, because the elevation doesn't change in that particular direction.
The directional derivative is a vector. The direction is whatever direction you're
talking about, and the magnitude is the rate of change in that direction.
The gradient is the vector that's simply the greatest positive directional derivative
at that point. Its direction is the direction of the steepest rise, and its magnitude
is the rate of rise in that direction.
If your hill is, say, a perfect cone, and you're on the side, then the gradient is the
vector from you straight toward the top, with magnitude equal to the slope of the
side of the cone. Any other vector is a directional derivative, with a smaller slope,
and it isn't the gradient.
What are the different elements of Boolean algebra?
The prototypical Boolean algebra; i.e. the Boolean algebra defined over the Boolean domain, has two elements in it: 0 and 1. For more information about Boolean algebra, please refer to the related link below.
The priority matrix, also known as the Eisenhower Matrix, is a time management tool that helps individuals and teams prioritize tasks based on their urgency and importance. It typically divides tasks into four quadrants: urgent and important, important but not urgent, urgent but not important, and neither urgent nor important. This visual framework aids in deciding which tasks to focus on, delegate, or eliminate, promoting more effective time allocation and productivity. By clarifying priorities, users can better manage their workload and reduce stress.
How do you prove that the sum of a rational number and its additive inverse is zero?
I can give you an example and prove it:
eg. take the rational no. 2......hence its additive inverse ie. its opposite no. will be -2
now lets add:
=(2)+(-2)
=2-2
=0
it means that the opposite no.s. get cancelled and give the answer 0
this is the same case for sum of a rational no. and its opposite no. to be ZERO
