Determine the kernel and range of each of thefollowing linear operators on R3: L (x) = (x3, x2, x1)T
Determine the kernel and range of each of thefollowing linear operators on R3: L (x) = (x3, x2, x1)T
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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Question
Determine the kernel and range of each of the
following linear operators on R3: L (x) = (x3, x2, x1)T
Expert Solution
Step 1
Null Space: The set of all vectors x such that is called the null space of the matrix A. This is
called the kernel of the matrix.
It is given that the linear transformation is . We can write the given transformation
as .
Step 2
We can write the given linear transformation in the matrix form as below:
The null space of the linear transformation is given by
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