Assume that T is a linear transformation. Find the standard matrix of T. T: R³→R², T(e,) = (1,4), and T (e,) =(-6,3), and T(e3) = (4, - 3), where e,, ez, and ez are the columns of the 3x3 identity ma

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Assume that T is a linear transformation. Find the standard matrix of T.

\[ T: \mathbb{R}^3 \to \mathbb{R}^2 \]

\[ T(\mathbf{e}_1) = (1, 4), \quad T(\mathbf{e}_2) = (-6, 3), \quad T(\mathbf{e}_3) = (4, -3) \]

where \(\mathbf{e}_1, \mathbf{e}_2,\) and \(\mathbf{e}_3\) are the columns of the 3 × 3 identity matrix.
Transcribed Image Text:Assume that T is a linear transformation. Find the standard matrix of T. \[ T: \mathbb{R}^3 \to \mathbb{R}^2 \] \[ T(\mathbf{e}_1) = (1, 4), \quad T(\mathbf{e}_2) = (-6, 3), \quad T(\mathbf{e}_3) = (4, -3) \] where \(\mathbf{e}_1, \mathbf{e}_2,\) and \(\mathbf{e}_3\) are the columns of the 3 × 3 identity matrix.
Expert Solution
Step 1

Given that: T: R3R2

Te1=1,4Te2=6,3Te3=4,3

Here e1, e2, e3 are  the columns of the 3x3 identity matrix.

To find the linear transformation T.

steps

Step by step

Solved in 5 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,