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1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C E-path] [ ī

1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C E-path] [ ī

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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1. Let \( B_1 = \left\{ \begin{bmatrix} 2 \\ 2 \end{bmatrix}, \begin{bmatrix} 1 \\ -2 \end{bmatrix} \right\} \) and \( B_2 = \left\{ \begin{bmatrix} -1 \\ 2 \end{bmatrix}, \begin{bmatrix} 3 \\ 0 \end{bmatrix} \right\} \) be two ordered bases for \( \mathbb{R}^2 \). i) Find \( \text{Rep}_{B_2}^{B_1} \) ii) Find \( \text{Rep}_{B_1}^{B_2} \) \[ \begin{bmatrix} 0 & 0 \\ c & 0 \end{bmatrix} \Rightarrow \begin{bmatrix} 0 & c \\ 6 & 6 \end{bmatrix} \begin{bmatrix} a & b \\ a & a \end{bmatrix} \begin{bmatrix} b & d \\ b & b \end{bmatrix} \]
Transcribed Image Text:1. Let \( B_1 = \left\{ \begin{bmatrix} 2 \\ 2 \end{bmatrix}, \begin{bmatrix} 1 \\ -2 \end{bmatrix} \right\} \) and \( B_2 = \left\{ \begin{bmatrix} -1 \\ 2 \end{bmatrix}, \begin{bmatrix} 3 \\ 0 \end{bmatrix} \right\} \) be two ordered bases for \( \mathbb{R}^2 \). i) Find \( \text{Rep}_{B_2}^{B_1} \) ii) Find \( \text{Rep}_{B_1}^{B_2} \) \[ \begin{bmatrix} 0 & 0 \\ c & 0 \end{bmatrix} \Rightarrow \begin{bmatrix} 0 & c \\ 6 & 6 \end{bmatrix} \begin{bmatrix} a & b \\ a & a \end{bmatrix} \begin{bmatrix} b & d \\ b & b \end{bmatrix} \]
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