(Linear algebra)3.Pls answer question asapWrite work neatly and box final answersThanks **Problem: Find the Matrix Representation**Find the matrix \( A' \) for \( T \) relative to the basis \( B' \).**Transformation:**\[ T: \mathbb{R}^3 \rightarrow \mathbb{R}^3, \quad T(x, y, z) = (x - y + 6z, 6x + y - z, x + 6y + z) \]**Basis:**\[ B' = \{ (1, 0, 1), (0, 2, 2), (1, 2, 0) \} \]**Instructions:**Put your answer in the array below. Use improper fractions where needed (for example, use \( \frac{4}{3} \) instead of \( 1 \frac{1}{3} \)).**Answer Array:**\[\begin{array}{ccc} & & \\ & & \\ & & \\\end{array}\]

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Answered: Find the matrix A' for T relative to…

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)

Pls answer question asap

Write work neatly and box final answers

Thanks

**Problem: Find the Matrix Representation**

Find the matrix \( A' \) for \( T \) relative to the basis \( B' \).

**Transformation:**
\[ T: \mathbb{R}^3 \rightarrow \mathbb{R}^3, \quad T(x, y, z) = (x - y + 6z, 6x + y - z, x + 6y + z) \]

**Basis:**
\[ B' = \{ (1, 0, 1), (0, 2, 2), (1, 2, 0) \} \]

**Instructions:**
Put your answer in the array below. Use improper fractions where needed (for example, use \( \frac{4}{3} \) instead of \( 1 \frac{1}{3} \)).

**Answer Array:**

\[
\begin{array}{ccc}
& & \\
& & \\
& & \\
\end{array}
\]

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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