Find the coordinate matrix of **x** in $ \mathbb{R}^n $ relative to the basis $ B' $.\[ B' = \{(8, 11, 0), (7, 0, 10), (1, 4, 6)\}, \quad \mathbf{x} = (-10, 23, -12) \]\[ [\mathbf{x}]_{B'} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_\end{bmatrix} \]Explanation:- You are asked to find the coordinates of the vector **x** relative to the different basis $ B' $.- The basis $ B' $ consists of three vectors: (8, 11, 0), (7, 0, 10), and (1, 4, 6).- The vector **x** is given as (-10, 23, -12).- The task involves expressing **x** as a linear combination of the vectors in $ B' $ and filling the coordinate matrix accordingly. The matrix on the right has three empty boxes implying that these will hold the coefficients from the linear combination of basis vectors.

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Find the coordinate matrix of x in R relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)}, x = (-10, 23, -12) [x]g = %3!

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Find the coordinate matrix of **x** in $ \mathbb{R}^n $ relative to the basis $ B' $.

\[ B' = \{(8, 11, 0), (7, 0, 10), (1, 4, 6)\}, \quad \mathbf{x} = (-10, 23, -12) \]

\[ [\mathbf{x}]_{B'} =
\begin{bmatrix}
\_\_ \\
\_\_ \\
\_\_
\end{bmatrix}
\]

Explanation:
- You are asked to find the coordinates of the vector **x** relative to the different basis $ B' $.
- The basis $ B' $ consists of three vectors: (8, 11, 0), (7, 0, 10), and (1, 4, 6).
- The vector **x** is given as (-10, 23, -12).
- The task involves expressing **x** as a linear combination of the vectors in $ B' $ and filling the coordinate matrix accordingly. The matrix on the right has three empty boxes implying that these will hold the coefficients from the linear combination of basis vectors.

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