() - ()а —bLet T : R? –→ R³ be defined by TLet a be thea2а — b,standard basis for R? and letB =1(a basis for R3).(a) Compute [T].(1) ()( )(b) Let y =(another basis for R²). Compute [T]½, and use23it to find [T

We find the matrix representation of given linear transformation with given basis:

(6) - () а —Ь Let T : R? →+ R³ be defined by T Let a be the a 2а — b, standard basis for R? and let () B = 1 2 (a basis for R³). (a) Compute [T]%. (b) Let y = (another basis for R²). Compute [T], and use it to find [T () ).

(6) - () а —Ь Let T : R? →+ R³ be defined by T Let a be the a 2а — b, standard basis for R? and let () B = 1 2 (a basis for R³). (a) Compute [T]%. (b) Let y = (another basis for R²). Compute [T], and use it to find [T () ).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

() - ()
а —b
Let T : R? –→ R³ be defined by T
Let a be the
a
2а — b,
standard basis for R? and let
B =
1
(a basis for R3).
(a) Compute [T].
(1) ()
( )
(b) Let y =
(another basis for R²). Compute [T]½, and use
2
3
it to find [T

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