Transformation Properties: Boost Your Knowledge

Recent questions in Transformation properties

Alexander Day 2022-02-13

Is the transformation $R_{\frac{π}{3}} (x)$ is linear transformation? Justify your answer.

Cherish Sellers 2022-02-13

If P is linear, then
1) None of the given options is correct
2) The null space of P is empty
3) $P (x - y) = P (x + y)$ for all inputs x,y
4) $P (a x + b y) = a P (x) + b P (y)$ for all inputs x, y and constants a, b.

Lawson Cain 2022-02-13

Determine the equation of the function with the following properties:
A transformation of the basic $y = \cot (x)$ function with
- A period of $\frac{π}{3}$
- A stretching factor of 3
- A phase shift to the left by straight $\frac{π}{12}$
- A vertical shift down by 5
Write the equation for the function described above:

Dillan Gibbs 2022-02-13

Constructing a transformation satisfying the given properties
Construct a transformation which maps the plane into the plane itself , and the curve $y = x^{2}$ onto the horizontal axis, and the line $y = 3$ onto the vertical axis.
I need to solve the set of equations
$T (x, x^{2}) = (x, 0)$
$T (x, 3) = (0, y)$
but couldn't. Any hints?

tlhalakq9 2022-02-13

Properties of $A^{T} A$ transformation.
Is it true a proposition for $3 \times 3$ real matrices A that if for a some nonzero vector v we have $A v \neq v$ and at the same time $(A^{T} A) v = v$ then for any vector u from $R^{3}$ we have $(A^{T} A) u = u$ (i.e. A is orthogonal) ?
Do we need assumption about full rank of the matrix A for this goal?
Can we extend the proposition for bigger dimensions?

Kiribatiyo2 2022-02-13

Rational scalar multiplication in Linear transformation using addition property [duplicate]
Linear transformation: Map $T : V \to W$ is said to be Linear transformation when it satisfy property:
1) $L (u + v) = L (u) + L (v) \forall u, v \in V$
2) $L (c v) = c L (v) \forall c \in F$
I know when $c \in N$ then property 2 can be obtained from property 1, since
$L (n v) = L (v) + L (v) \dots . . + L (v)$ (n times where $n \in N)$
Now I have read in somewhere that if our scalar c is rational then property 2 also follows from property 1, but I am unable to prove this. How can I show that if $c \in Q$ , when (2) follows from (1)?
I know that if our scalar is irrational, then we cannot use property 1 to prove property 2.

Pegov1 2022-02-12

Linear transformation with special properties
Linear transformation $f : R^{10} \to R^{7}$ has an attribute that every vector v for which is true that $f (v) = 0$ is in linear span ${(1, 2, \dots, 10)}^{T}, {(1, 1 \dots, 1)}^{T} >$ . Create such transformation or prove that it doesn't exists.

beyondthegametcm 2022-02-12

The function:
$f (x) = e^{x + 1} - 2$
a) Domain
b) Range
c) x, y-intercepts
d) Sketch a graph of f
e) What transformations happened to $y = e^{x}$ to get $f (x) ?$

legurl083ra 2022-02-12

What are Bezier curves?

Marlee Yates 2022-02-12

$L^{- 1} [\frac{s}{{(s + 3)}^{2} + 9}]$

Racetovb4j 2022-02-12

Find the Laplace Transform of the following
$f (8 t - 13)$

Fastage6bk 2022-02-12

Invariance of $d s^{2}$ and transformation properties of ${d x}^{i}$
Invariance of $d s^{2}$ and transformation properties of ${d x}^{i}$
$d s^{^{'} 2} = d s^{2}$
$g_{i j}^{^{'}} {d x}^{^{'} i} {d x}^{^{'} j} = g_{i j}^{^{'}} \frac{\partial x^{^{'} j}}{\partial x^{k}} {d x}^{k} \frac{\partial x^{^{'} j}}{\partial x^{l}} {d x}^{l}$
$= g_{i j}^{^{'}} \frac{\partial x^{^{'} i}}{\partial x^{k}} \frac{\partial x^{^{'} j}}{{d x}^{l}} {d x}^{k} {d x}^{l}$
$= g_{k l} {d x}^{k} {d x}^{l}$
where $g_{i j}$ is metric tensor
1) I want to ask that idea behind this transformation is because distance remains invariant under transformation to different coordinate system
2) How this new variable k,l are introduced the text i am reading is physics pages

Jessica Collier 2022-02-12

Examine transformation properties of functions under symmetry operations
I need help learn how to examine transformation of a functions under a symmetry operation. For example, applying reflection in x axis on a vector (x,y)
$(x, y) . [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}] = (x, - y)$
from which we know how x and y transform under reflection. My question is how to examine what happens to other functions such as $x^{2}, x y, x^{2} + y^{2}$ .. etc, under the same operation? Also, how to find matrix representations of the operation for these functions?

kzae220o3 2021-11-23

State the parent function, transformations, domain and range.

Douglas Kraatz 2021-11-23

Write a rule to describe each transformation

vetrila10 2021-11-22

State the parent function, transformations, domain and range.

Nefissi8u 2021-11-22

The graph shows one of the six basic functions of graphs and a ransformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.

ambiguit 2021-11-22

Answer true or false to each of the following statement and explain your answer.
In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.

Tomasettiq3 2021-11-22

Answer true or false to the following statement and explain your answer.
Any scatterplot that exhibits curvature can be straightened by the method of transformations.

deliriwmfg 2021-11-21

What is the new equation for the pictured graph after transformations from the parent function f(x)=lxl showing the transformations

These integral calculations and transformation properties are always used in Jira, Python, Java, and many other types of applied programming when you need to apply 2D or 3D transformations of an object. When you need to work with the linear transformation properties by applying specific equations, you will find the collection of questions and answers helpful. When you need to provide graphical lab reports, make sure that you focus on the transformation properties as you design your assignment. Take a look at some examples to see the logic of how to write down transformations and explain the changes in motion.

Integral Calculus

Linear Transformation Properties: Expert Help & Solutions