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Let ū, = (1,0,0), ü, = (2,–1,1), ū, = (0,1,1), and transformation T : R' → R´ be A 1 1 multiplication by the matrix A = 0 -3 Determine if the set {Tu,, Tu,,Tu;} is linearly 12 2 2 independent or not.

Let ū, = (1,0,0), ü, = (2,–1,1), ū, = (0,1,1), and transformation T : R' → R´ be A 1 1 multiplication by the matrix A = 0 -3 Determine if the set {Tu,, Tu,,Tu;} is linearly 12 2 2 independent or not.

Advanced Engineering Mathematics
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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Let \(\mathbf{u}_1 = (1, 0, 0)\), \(\mathbf{u}_2 = (2, -1, 1)\), \(\mathbf{u}_3 = (0, 1, 1)\), and transformation \(T_A: \mathbb{R}^3 \rightarrow \mathbb{R}^3\) be multiplication by the matrix \(A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 0 & -3 \\ 2 & 2 & 0 \end{bmatrix}\). Determine if the set \(\{ T\mathbf{u}_1, T\mathbf{u}_2, T\mathbf{u}_3 \}\) is linearly independent or not.
Transcribed Image Text:Let \(\mathbf{u}_1 = (1, 0, 0)\), \(\mathbf{u}_2 = (2, -1, 1)\), \(\mathbf{u}_3 = (0, 1, 1)\), and transformation \(T_A: \mathbb{R}^3 \rightarrow \mathbb{R}^3\) be multiplication by the matrix \(A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 0 & -3 \\ 2 & 2 & 0 \end{bmatrix}\). Determine if the set \(\{ T\mathbf{u}_1, T\mathbf{u}_2, T\mathbf{u}_3 \}\) is linearly independent or not.
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