Transformation Properties: Boost Your Knowledge

Recent questions in Transformation properties

Anish Buchanan 2021-01-06

Use a counterexample to show that the statement is false.
$T : R^{2} \to R^{2}, T (x_{2}, x_{2}) = (x_{1} + 4, x_{2})$ is a linear transformation?

generals336 2021-01-04

The solution of initial value problem $y^{″} + 2 y^{'} + 2 y = δ (t - π), y (0) = 0, y^{'} (0) = 1$ and draw the graph of the solution.

jernplate8 2021-01-04

Whether the statement “ Let A be an $m \times n$ matrix.
The system $A x = b is consistent for all b in R^{m} if and only if the columns of A form a generating set for R^{m}$ " is true or false.

CoormaBak9 2020-12-31

Prove the relation $T = S .$

permaneceerc 2020-12-31

Prove the difference of any even integer minus any odd integer is odd.

necessaryh 2020-12-29

The equation for inverse function $g^{- 1} (x) for the function g (x) = \sqrt{x + 2}$ .

chillywilly12a 2020-12-17

Define a solution the given initial-value problem.
$4^{″} + 4 y^{'} 4 y = δ (t - 4)$
$y (0) = 1$
$y^{'} (0) = 2$

Haven 2020-12-15

Prove whether $f : R \to R defined by f (x) = 4 x - 2$ is a linear transformation.
Prove whether $f : R \to R defined by f (x) = 2 x$ is a linear transformation.
Which one equivalent to the linear transformation $T : R \to R defined by T (1) = 2 ?$

babeeb0oL 2020-12-15

Find and describe an example of a matrix with each of the following properties.
Briefly describe why the desired property is in the matrix you picked. If no such matrix exists, explain using a theorem studied.
(a) A square matrix representing an injective but not a surjective transformation.

Khaleesi Herbert 2020-12-14

To state:
The solution of the given initial value problem using the method of Laplace transforms.
Given:
The initial value problem is,
$y + 6 y^{'} + 5 y = 12 e^{t}, y (0) = - 1, y^{'} (0) = 7$

CoormaBak9 2020-12-13

To state:
The solution of the given initial value problem using the method of Laplace transforms.
Given:
The initial value problem is,
$y + 2 y^{'} + 5 y = 0, y (0) = 2, y^{'} (0) = 4$

Ayaana Buck 2020-12-03

Define Transformation? Write down the properties of Linear transformation and rotational transformation.

Tammy Todd 2020-12-01

a) To find:
The images of the following points under under a $90^{\circ}$ rotation counterclockwise about the origin:
I. $(2, 3)$
II. $(- 1, 2)$
III, (m,n) interms of m and n
b)To show:
That under a half-turn with the origin as center, the image of a point $(a, b) has coordinates (- a, - b) .$
c) To find:
The image of $P (a, b) under the rotation clockwise by 90^{\circ}$ about the origin.

babeeb0oL 2020-11-30

Assum T: $R_{m}$ to $R_{n}$ is a matrix transformation with matrix A. Prove that if the columns of A are linearly independent, then T is one to one (i.e injective). (Hint: Remember that matrix transformations satisfy the linearity properties.
Linearity Properties:
If A is a matrix, v and w are vectors and c is a scalar then
$A 0 = 0$
$A (c v) = c A v$
$A (v + w) = A v + A w$

Emeli Hagan 2020-11-23

To find: The solution of the given initial value problem.

Josalynn 2020-11-23

The solution of the initial value problem $y^{″} + 4 y = 2 δ (t - π / 4), y (0) = 0, y^{'} (0) = 0$ and draw the graph of the solution.

Tabansi 2020-11-14

To calculate : The reduced form of the provided matrix, $[\begin{matrix} 1 & 0 & 4 & 0 \\ 0 & 1 & - 3 & - 1 \\ 0 & 0 & - 2 & 2 \end{matrix}]$ with the use of row operations.

DofotheroU 2020-11-12

The values of a for which the given matrix is invertible.

Tabansi 2020-11-10

Determine if a linear transformation function is
$T : M_{33},$
$T (A) = [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}] A$

BolkowN 2020-11-05

Let $T : U \to U$ be a linear transformatiom and let
$B$ be a basis of U. Define the determanant det (T) of T as
$d e t (T) = d e t ([T] B) .$
Show that det (T) is well=defined, i.e. that it does not depend on the choice of the basis $B .$
Prove that T is invertible if and only if det $(T) \neq 0.$ If T is invertible, show that
$d e t (T^{- 1}) = \frac{1}{d e t (T)} .$

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