Finding the Kernel, Nullity, Range, and Rank In Exercises 35-38, define the linear transformation T by T ( v ) = A v . Find (a) ker ( T ) , (b) nullity ( T ) , (c) range ( T ) , and (d) rank ( T ) . A = [ 1 1 − 1 1 2 1 0 1 0 ]
Finding the Kernel, Nullity, Range, and Rank In Exercises 35-38, define the linear transformation T by T ( v ) = A v . Find (a) ker ( T ) , (b) nullity ( T ) , (c) range ( T ) , and (d) rank ( T ) . A = [ 1 1 − 1 1 2 1 0 1 0 ]
Solution Summary: The author explains the mathrmker(T) for the given matrix.
Finding the Kernel, Nullity, Range, and Rank In Exercises 35-38, define the linear transformation T by
T
(
v
)
=
A
v
. Find (a)
ker
(
T
)
, (b)
nullity
(
T
)
, (c)
range
(
T
)
, and (d)
rank
(
T
)
.
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
Chapter 6 Solutions
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