1 2 1 1 1 with respect to the basis B = of M22" Find the coordinate vector of A = 3 4 [A]g =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Problem Statement:**

Find the coordinate vector of \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) with respect to the basis \( B = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \right\} \) of \( M_{22} \).

**Diagram Explanation:**

- On the left side, there is a column filled with empty boxes labeled \([A]_B =\). These boxes are meant to contain the entries of the coordinate vector of matrix \( A \) with respect to the basis \( B \).

**Call to Action:**

- At the bottom left corner, there is a button labeled "Need Help?” with a smaller button below it labeled "Read It", suggesting resources or further explanations can be accessed by clicking these elements.
Transcribed Image Text:**Problem Statement:** Find the coordinate vector of \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) with respect to the basis \( B = \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}, \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \right\} \) of \( M_{22} \). **Diagram Explanation:** - On the left side, there is a column filled with empty boxes labeled \([A]_B =\). These boxes are meant to contain the entries of the coordinate vector of matrix \( A \) with respect to the basis \( B \). **Call to Action:** - At the bottom left corner, there is a button labeled "Need Help?” with a smaller button below it labeled "Read It", suggesting resources or further explanations can be accessed by clicking these elements.
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