Finding the Standard Matrix and the Image In Exercises 2 3 - 2 6 , (a) find the standard matrix A for the linear transformation T and (b) use A to find the image of the vector v . Use a software program or a graphing utility to verify your result. T ( x , y , z ) = ( 2 x + 3 y − z , 3 x − 2 z , 2 x − y + z ) , v = ( 1 , 2 , − 1 )
Finding the Standard Matrix and the Image In Exercises 2 3 - 2 6 , (a) find the standard matrix A for the linear transformation T and (b) use A to find the image of the vector v . Use a software program or a graphing utility to verify your result. T ( x , y , z ) = ( 2 x + 3 y − z , 3 x − 2 z , 2 x − y + z ) , v = ( 1 , 2 , − 1 )
Solution Summary: The author explains how the standard matrix is formed as A for T(x,y,z) = 'left'.
Finding the Standard Matrix and the Image In Exercises
2
3
-
2
6
, (a) find the standard matrix
A
for the linear transformation
T
and (b) use
A
to find the image of the vector
v
. Use a software program or a graphing utility to verify your result.
T
(
x
,
y
,
z
)
=
(
2
x
+
3
y
−
z
,
3
x
−
2
z
,
2
x
−
y
+
z
)
,
v
=
(
1
,
2
,
−
1
)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
v - (-9, 2) is transformed using the transformation matrix A =
What is the resulting vector? Show all your work.
Explain how to determine whether a function T : V → W is a linear
transformation. Secondly give some example along with proper explanation where this T can
be treated as matrix.
Chapter 6 Solutions
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY