4,5,6 1. For the following linear transformation, T,Tin mamubo sinW1 = 3x1 - 6x2 + 2x3W2 = -2x1 +4x2 + X3W3 = x1-2x2 – x3W4 = -X1 + 2x2 + 2x3i)Find the matrix that represents this transformation.ii)Determine the domain of T.o aielox Soino T a (vixiii)Determine the codomain of T.iv)Find a basis for ker(T).(vx)v)Determine the dimension of the ker(T).vi)Find a basis for range(T).iaceen o nielo ono-ot-ono T (rvii)Determine the dimension of the range(T).viii)Is T a one-to-one mapping? Explain your reasoning.ix)Is T an onto mapping? Explain your reasoning.l itDetermine whether the linear transformation defined by the equations isinvertible; if so, find the standard matrix for the inverse transformation, and findT. If it is not invertible, explain why.x)

Name: 4,5,6 1. For the following linear transformation, T,Tin mamubo sinW1 =
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Description: 4,5,6 1. For the following linear transformation, T,Tin mamubo sinW1 = 3x1 - 6x2 + 2x3W2 = -2x1 +4x2 + X3W3 = x1-2x2 – x3W4 = -X1 + 2x2 + 2x3i)Find the matrix that represents this transformation.ii)Determine the domain of T.o aielox Soino T a (vixiii

Given Transformation convert to the matrix T(w)= 3-6 2-2 4 1 1-2-1-1 2 2 Transform the matrix to…

Answered: iv) Find a basis for ker(T). 1o lamsd…

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iv) Find a basis for ker(T). 1o lamsd zied v) Determine the dimension of the ker(T). vi) Find a basis for range(T). iaceem aoieig1Sono-ot-on vii) Determine the dimension of the range(T).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

4,5,6

1. For the following linear transformation, T,
Tin mamubo sin
W1 = 3x1 - 6x2 + 2x3
W2 = -2x1 +4x2 + X3
W3 = x1-2x2 – x3
W4 = -X1 + 2x2 + 2x3
i)
Find the matrix that represents this transformation.
ii)
Determine the domain of T.
o aielox Soino T a (vix
iii)
Determine the codomain of T.
iv)
Find a basis for ker(T).
(vx)
v)
Determine the dimension of the ker(T).
vi)
Find a basis for range(T).
iaceen o nielo ono-ot-ono T (r
vii)
Determine the dimension of the range(T).
viii)
Is T a one-to-one mapping? Explain your reasoning.
ix)
Is T an onto mapping? Explain your reasoning.
l it
Determine whether the linear transformation defined by the equations is
invertible; if so, find the standard matrix for the inverse transformation, and find
T. If it is not invertible, explain why.
x)

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