6. Write True or False.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
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6. Write True or False.
a) A vector b is a linear combination of the columns of a matrix A if and only if the equation
Ax = b has at least one solution.
b) If A is 3x 5 matrix and T is a transformation defined by T(x)= Ax , then the domain of T
is R.
c) If AB = BA and if A is invertible, then AB = BA'.
d) The differential equation
* = Vxy+Jxy is a Bernoulli differential equation.
dx
e) If T: R* → R" is a linear transformation with matrix A, then Rng(T) is the column
Transcribed Image Text:6. Write True or False. a) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. b) If A is 3x 5 matrix and T is a transformation defined by T(x)= Ax , then the domain of T is R. c) If AB = BA and if A is invertible, then AB = BA'. d) The differential equation * = Vxy+Jxy is a Bernoulli differential equation. dx e) If T: R* → R" is a linear transformation with matrix A, then Rng(T) is the column
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