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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 does truncate mean in math terms?
truncate means to add the whole number to whatever else you have,and then multiply it by your fraction
How do you multiply 3x3 matrices by 1x3 or 3x1?
First of all, if we have any two matrices of sizes mxn and pxq where m, n, p and q are natural numbers, then we must have n=p to be able to multiply the matrices. The result is an mxq matrix.
For example, a 3x1 matrix has m=3 and n=1. We can multiply it with any matrix of size 1xq. For example a 2x3 matrix can be multiplied with a 3x1 matrix which has 3 rows and 1 column and the result is a 2x1 matrix. (2x3) multiplies by (3x1) gives a (2x1) matrix. The easy way to remember this is write the dimension of Matrix A and then Matrix B. The two inner numbers must be the same and the two outer numbers are the dimensions of the matrix you have after multiplication.
For example Let Matrix A have dimensions (axb) multiply it by matrix B which has dimensions (bxc) = the result is matrix of dimensions ac. Using the trick we would remind ourselves by writing (a,b)x(b,c)=(a,c). This is technically wrong because the numbers are dimensions, but it is just a method to help students remember how to do it.
So, a 3x3 matrix can be multiplied by a 3x 1 but not by a 1,3 matrix.
How do you do it? Just multiply each entry in the first row of A by each entry in the first column of B and add the products. Do the same for the next row etc.
Many (or should I honestly say MOST) people use their fingers and go along row one and then down column one. The add the products of the entries as they do that. Then they do the same for row two and column two etc. It really does help!
What are the properties of a group?
In abstract algebra, the properties of a group G under a certain operation are:
- Associativity: (ab)c = a(bc) for all a, b and c belonging to G
- Identity: Identity e belongs to G.
- Inverse: If ab = ba = a, where a is the identity, then b is the inverse of a.
How many numbers can 15 go into?
The answer is Infinity. Numbers keep going up and up and never stop. Therefore fifteen will keep going into a bigger number each time. HOWEVER, if you meant 'how many numbers go into fifteen' , the answer would be 4. Four numbers (1,3,5 and 15) go into 15.
How do you turn a question into an equation?
It depends on what the question is and what level of mathematics you have mastered.
(n^2-n)/2-1
How many gallons to fill up a truck with a V8 engine?
There is no direct relationship between the number of cylinders in an engine and the size of its fuel tank!
There can be no equivalence.
An inch is a measure of length or distance in 1-dimensional space while an ounce is a measure of mass. The two measure different things and, according to basic principles of dimensional analysis, any attempt at conversion from one to the other is fundamentally flawed.
To find the value of n
-7n=63
n=63/-7
n-9
Hence,-9 is the required answer.
What are the multiplies of 15?
They are elements of the infinite set of numbers of the form 15*k where k is an integer.
75 pounds of the 80 cent nuts and 15 of the 50 cent nuts.
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 is the difference between a postulate and theorem in Geometry?
A postulate is assumed to be true while a theorem is proven to be true. The truth of a theorem will be based on postulates.
What type of triangle has side lengths of 23 24and 24?
An isoceles triangle! It has two lengths the same!
What does terms of an expression mean?
An expression is a collection of numbers and variables, along with mathematical operations, but without an equality (or inequality) symbol.
