Question

asked 2020-10-20

In this problem, allow \(T_1: \mathbb{R}^2 \rightarrow \mathbb{R}^2\) and \(T_2: \mathbb{R}^2 \rightarrow \mathbb{R}^2\) be linear transformations. Find Ker(T_1), Ker(T_2), Ker(T_3) of the respective matrices:

\(A=\begin{bmatrix}1 & -1 \\-2 & 0 \end{bmatrix} , B=\begin{bmatrix}1 & 5 \\-2 & 0 \end{bmatrix}\)

\(A=\begin{bmatrix}1 & -1 \\-2 & 0 \end{bmatrix} , B=\begin{bmatrix}1 & 5 \\-2 & 0 \end{bmatrix}\)

asked 2021-03-02

Let T \(\displaystyle{P}_{{2}}\rightarrow\mathbb{R}^{{3}}\) be a transformation given by

\(\displaystyle{T}{\left({f{{\left({x}\right)}}}\right)}={\left[\begin{array}{c} {f{{\left({0}\right)}}}\\{f{{\left({1}\right)}}}\\{2}{f{{\left({1}\right)}}}\end{array}\right]}\)

(a)Then show that T is a linear transformation.

(b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T.

(c)Show that T is one-to-one.

\(\displaystyle{T}{\left({f{{\left({x}\right)}}}\right)}={\left[\begin{array}{c} {f{{\left({0}\right)}}}\\{f{{\left({1}\right)}}}\\{2}{f{{\left({1}\right)}}}\end{array}\right]}\)

(a)Then show that T is a linear transformation.

(b)Find and describe the kernel(null space) of T i.e Ker(T) and range of T.

(c)Show that T is one-to-one.

asked 2021-03-11

An object of mass M is held in place by an applied force Fand A pulley system as shown in Figure. The pulleys aremassless and frictionless. Find (a) the tension in each section of rope, \(\displaystyle{T}_{{1}},{T}_{{2}},{T}_{{3}},{T}_{{4}}\) and \(\displaystyle{T}_{{5}}\) and b) the magnitude of F. Suggestion: Draw afree-body diagram for each pulley.

asked 2020-11-08

Determine the transformations of the function f(x) to get the function \(g(x) =1/2f(5(x−3))−12\) (The transformations happen in c, b, a, d order)

asked 2021-02-11

Your friend attempted to describe the transformations applied to the graph of \(y=sinx\) to give the equation \(f(x)=1/2sin(-1/3(x+30))+1\).

They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.

a) f(x) has been reflected vertically.

b) f(x) has been stretched vertically by a factor of 2.

c) f(x) has been stretched horizontally by a factor of 3.

d) f(x) has a phase shift left 30 degrees.

e) f(x) has been translated up 1 unit.

They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.

a) f(x) has been reflected vertically.

b) f(x) has been stretched vertically by a factor of 2.

c) f(x) has been stretched horizontally by a factor of 3.

d) f(x) has a phase shift left 30 degrees.

e) f(x) has been translated up 1 unit.

asked 2020-11-23

Consider the scatterplot of y versus x in Output B.6 above.

a. Which power transformations on y should be considered to straighten the scatterplot?

b. Which power transformations on x should be considered to straighten the scatterplot?

a. Which power transformations on y should be considered to straighten the scatterplot?

b. Which power transformations on x should be considered to straighten the scatterplot?

asked 2021-02-23

List a sequence of transformations, in words, to convert the graph of \(f(x)=x^2\) into the graph of \(g(x)=-6(x-2)^2+5\).

asked 2021-02-03

Lily wants to define a transformation (or series of transformations) using only rotations, reflections or translations that takes Figure A to Figure B.

Which statement about the transformation that Lily wants to define is true?

A. It can be defined with two reflections.

B.It can be defined with one rotation and one translation.

C. It cannot be defined because Figure A and Figure B are not congruent.

D.It cannot be defined because the longest side of Figure B is on the bottom.

Which statement about the transformation that Lily wants to define is true?

A. It can be defined with two reflections.

B.It can be defined with one rotation and one translation.

C. It cannot be defined because Figure A and Figure B are not congruent.

D.It cannot be defined because the longest side of Figure B is on the bottom.

asked 2020-11-22

Answer true or false to each of the following statements and explain your answers.

a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.

b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.

c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.

a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.

b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.

c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.

asked 2020-11-22

Functions f and g are graphed in the same rectangular coordinate system. If g is obtained from f through a sequence of transformations, find an equation for g.

(Graph given on the link)

(Graph given on the link)