Linear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation T : R n → R m by T ( v ) = A v . Use the matrix A to (a) determine the dimensions of R n and R m , (b) find the image of v, and (c) find the preimage of w. A = [ 4 0 0 5 1 1 ] , v = ( 2 , 2 ) , w = ( 4 , − 5 , 0 )
Linear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation T : R n → R m by T ( v ) = A v . Use the matrix A to (a) determine the dimensions of R n and R m , (b) find the image of v, and (c) find the preimage of w. A = [ 4 0 0 5 1 1 ] , v = ( 2 , 2 ) , w = ( 4 , − 5 , 0 )
Solution Summary: The author explains how to determine the dimensions of Rn, and the vectors in the matrix.
Linear Transformation Given by a Matrix In Exercises 23-28, define the linear transformation
T
:
R
n
→
R
m
by
T
(
v
)
=
A
v
. Use the matrix A to (a) determine the dimensions of
R
n
and
R
m
, (b) find the image of v, and (c) find the preimage of w.
A
=
[
4
0
0
5
1
1
]
,
v
=
(
2
,
2
)
,
w
=
(
4
,
−
5
,
0
)
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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
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term
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