## Linear Transformation and Null Space**Problem Statement:**Let $ T $ be a linear transformation represented by:\[ T = \begin{bmatrix} -3 & 10 & -9 \\ -3 & 8 & -10 \end{bmatrix} \]A nonzero vector in the null space is $ \langle \quad, \quad, \quad \rangle $ (Enter the components of a NONZERO vector in the null space).**Instructions:**- Find a nonzero vector that, when multiplied by the transformation matrix $ T $, results in the zero vector.- Enter the components of this nonzero vector in the provided boxes.**Navigation:**- Click the "Next Question" button to proceed to the subsequent question.**Explanation:**This problem involves finding a vector in the null space of the given linear transformation matrix $ T $. Specifically, we are searching for a vector $ \mathbf{x} $ such that $ T\mathbf{x} = \mathbf{0} $, where $ \mathbf{0} $ is the zero vector. The null space of a matrix consists of all vectors that satisfy this condition. Keep in mind that we are looking for a nonzero vector, implying that the result should not be the trivial solution where all components are zero. Use algebraic methods or computational tools to determine the appropriate vector and fill in the blanks accordingly.

We need to find a non zero vector such that Tx = 0.

Answered: Let T be a linear transformation…

Let T be a linear transformation represented by -3 10 -9 T = -3 8 - 10 A nonzerovector in the null space is (Enter the components of a NONZERO vector in the nullspace)

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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Question

## Linear Transformation and Null Space

**Problem Statement:**

Let $ T $ be a linear transformation represented by:

\[ T = \begin{bmatrix} -3 & 10 & -9 \\ -3 & 8 & -10 \end{bmatrix} \]

A nonzero vector in the null space is $ \langle \quad, \quad, \quad \rangle $ (Enter the components of a NONZERO vector in the null space).

**Instructions:**
- Find a nonzero vector that, when multiplied by the transformation matrix $ T $, results in the zero vector.
- Enter the components of this nonzero vector in the provided boxes.

**Navigation:**
- Click the "Next Question" button to proceed to the subsequent question.

**Explanation:**
This problem involves finding a vector in the null space of the given linear transformation matrix $ T $. Specifically, we are searching for a vector $ \mathbf{x} $ such that $ T\mathbf{x} = \mathbf{0} $, where $ \mathbf{0} $ is the zero vector. The null space of a matrix consists of all vectors that satisfy this condition.

Keep in mind that we are looking for a nonzero vector, implying that the result should not be the trivial solution where all components are zero. Use algebraic methods or computational tools to determine the appropriate vector and fill in the blanks accordingly.

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