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.
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.
v - (-9, 2) is transformed using the transformation matrix A =
What is the resulting vector? Show all your work.
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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