Transcribed Image Text:**Topic: Coordinate Matrix in Linear Algebra**
Find the coordinate matrix of **x** in \( \mathbb{R}^n \) relative to the basis \( B' \).
Given:
- \( B' = \{(9, 0), (0, 7)\} \)
- \( \mathbf{x} = (27, 28) \)
We need to find \([\mathbf{x}]_{B'}\).
**Diagram Explanation:**
The diagram shows a 2x1 matrix setup:
\[
[\mathbf{x}]_{B'} = \begin{bmatrix}
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
- The empty boxes represent the components of the coordinate matrix which need to be determined.
- The arrows suggest the direction of solving or component extraction: horizontal and vertical, possibly indicating how the basis vectors influence the coordinates of **x**.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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![**Topic: Coordinate Matrix in Linear Algebra**
Find the coordinate matrix of **x** in \( \mathbb{R}^n \) relative to the basis \( B' \).
Given:
- \( B' = \{(9, 0), (0, 7)\} \)
- \( \mathbf{x} = (27, 28) \)
We need to find \([\mathbf{x}]_{B'}\).
**Diagram Explanation:**
The diagram shows a 2x1 matrix setup:
\[
[\mathbf{x}]_{B'} = \begin{bmatrix}
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
- The empty boxes represent the components of the coordinate matrix which need to be determined.
- The arrows suggest the direction of solving or component extraction: horizontal and vertical, possibly indicating how the basis vectors influence the coordinates of **x**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc42b80bf-a5d4-414b-bce1-0fe52a04dbbd%2F1e0ab4cb-2699-4a79-898e-7b4170eda7ad%2Fd2tzbpb_processed.png&w=3840&q=75)
