Match each differential equation in the first column with the corresponding type in the second column. (Multiple entries in the first column may correspond to the same entry from the second column.) For technical reasons, the equivalence class of a will be denoted by ā in the first column, and it will be denoted by [a] in the second column. (ā = [a] For instance, 2 = [2]) %3D L2 is Seç. (3) Z12 has Seç. (3) The ideal (3) of Z12 is Seç. The elements of the ideal (3) of Z12 are (3) Seç. Z12 is The element 2 + (3) of (3) Seç.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![Seç.
is a zero divisor.
is a field and an integral domain.
is a maximal ideal but not a prime ideal.
is a prime and maximal ideal.
The kernel of f is a prime ideal.
:5
V The kernel of f is an ideal of S.
The kernel of f is a maximal ideal.
has at least one zero divisor.
are [0], [1], [2], [3].
is neither a maximal nor a prime ideal.
Match each differential equation in the first has no zero divisor.
is not invertible.
is neither a field nor a integral domain.
is a field but not an integral domain.
are [0], [1], [2].
second column.
(Multiple entries in the first column may co
column.)
For technical reasons, the equivalence class is invertible.
it will be denoted by [a] in the second colu is a prime ideal but not a maximal ideal.
(ā = [a] For instance,
ar
[2])
is an integral domain but not a field.
are [0], [3], [6], [9], [12], [15], [18], .
are [0], [3], [6], [9].
is
(3)
Seç.
Z12
has
(3)
Seç.
The ideal (3) of Z12 is
Seç.
The elements of the ideal (3) of
are
Seç.
(3)
Z12
The element 2+ (3) of
is
(3)
Seç.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd367c4ac-aebb-4fba-804e-d05513f56c25%2F9575ca51-7dcf-4b60-8bfe-3ade364b4189%2F5wi2anq_processed.jpeg&w=3840&q=75)
![Match each differential equation in the first column with the corresponding type in the
second column.
(Multiple entries in the first column may correspond to the same entry from the second
column.)
For technical reasons, the equivalence class of a will be denoted by ā in the first column, and
it will be denoted by [a] in the second column.
[a] For instance, 2 = [2].)
is
(3)
Seç.
has
(3)
Seç.
The ideal (3) of Z12 is
Seç.
The elements of the ideal (3) of
Z12
(3)
are
Seç.
Z12
The element 2 + (3) of
is
Seç.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd367c4ac-aebb-4fba-804e-d05513f56c25%2F9575ca51-7dcf-4b60-8bfe-3ade364b4189%2Fnpkdmqa_processed.jpeg&w=3840&q=75)
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