1. **Linear transformation** \( T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) is given by\[T \left( \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \right) = \begin{bmatrix} -3x_1 + 5x_2 \\ 2x_1 - 3x_2 \\ 2x_3 \end{bmatrix}.\] (a). Find the standard matrix for \( T \). (b). Find the inverse of \( T \).---2. **Given** \[A = \begin{bmatrix} 1 & 4 & 0 & 0 & -3 \\ 0 & -3 & 1 & 0 & 5 \\ 1 & 7 & -1 & 1 & -4 \\ 0 & -3 & 1 & 1 & -4 \end{bmatrix}\] (a). Find the RREF of \( A \). (b). Find a basis for \( \text{Col } A \). (c). Find a basis for \( \text{Row } A \). (d). Find a basis for \( \text{Nul } A \). (e). What is the dimension of \( \text{Row } A \)? What is the dimension of \( \text{Nul } A \)? What is \( \text{rank}(A) \)?

-31 + 5x2 1. Linear transformation T : R³ → R³ is given by T 2æ1 – 3x2 2x3 |(a). Find the standard matrix for T. (ь) Find the inverse of T. 4 -3 -3 1 2. Given A 1 7 -1 1 -4 | 0 -3 1 1 -4 (a). Find the RREF of A. (Ь). Find a basis for Col A. (c). Find a basis for RowA. (d). Find a basis for NulA. (e). What is the dimension of Row A? What is the dimension of NulA? What is rank(A) ?

-31 + 5x2 1. Linear transformation T : R³ → R³ is given by T 2æ1 – 3x2 2x3 |(a). Find the standard matrix for T. (ь) Find the inverse of T. 4 -3 -3 1 2. Given A 1 7 -1 1 -4 | 0 -3 1 1 -4 (a). Find the RREF of A. (Ь). Find a basis for Col A. (c). Find a basis for RowA. (d). Find a basis for NulA. (e). What is the dimension of Row A? What is the dimension of NulA? What is rank(A) ?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Linear Algebra. Please write your answer clearly. Thanks.
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