Suppose that T : R4 → R4 is a linear map such that
T (e1 − e2) = e1, T (e2 − e3) = e2, T (e3 − e4) = e3, T (e4 + e1) = e4.
(a) Find the matrix of T

To find the matrix representation of the linear map \( T: \mathbb{R}^4 \to \mathbb{R}^4 \), we will follow these steps:

### Step 1: Set up the standard basis vectors for \( \mathbb{R}^4 \)
Let \( e_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}, e_2 = \begin{pm

Suppose that T : R4 → R4 is a linear map such that T(e1 − e2) = e1, T(e2 − e3) = e2, T(e3 − e4) = e3, T(e4 + e1) = e4. (a) Find the matrix of T.

This page provides a step-by-step solution to finding the matrix of a linear transformation T: R4 → R4, given the transformations of basis vectors. Explore linear algebra concepts, matrix representation, and the use of standard basis vectors.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation