Let A be a 2 x 3 matrix and T: R³ → R² be the linear mapping T (7) = A 7. 2 (6) - A) ¹ (1) - ()-[²] T - and T Given that T absin (a) f ?х ∞ a sl find A.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 23E: Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find...
Question
Let A be a 2 x 3 matrix and T: R³ → R2 be the linear mapping T
(E)--(8)
=
T
Given that T
absin (a)
di
f
8
α Ω
= [3]. ar
, and T
= A x.
2
(1)-1)
=
x
P
, find A.
Transcribed Image Text:Let A be a 2 x 3 matrix and T: R³ → R2 be the linear mapping T (E)--(8) = T Given that T absin (a) di f 8 α Ω = [3]. ar , and T = A x. 2 (1)-1) = x P , find A.
Expert Solution
Step 1: Given

Consider the linear transformation  T colon R cubed rightwards arrow R squared 

T left parenthesis x right parenthesis equals A x

T open parentheses table row 1 row 0 row 0 end table close parentheses equals open square brackets table row 1 row 7 end table close square brackets
T open parentheses table row 0 row 1 row 0 end table close parentheses equals open square brackets table row 3 row 0 end table close square brackets
T open parentheses table row 0 row 0 row 1 end table close parentheses equals open square brackets table row 2 row cell negative 5 end cell end table close square brackets


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