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Let -8 -2 -9 +1- 6 4 4 0 4 True False A = Is it true that w is in Nul(A)? 8 and w= 1 H

Let -8 -2 -9 +1- 6 4 4 0 4 True False A = Is it true that w is in Nul(A)? 8 and w= 1 H

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
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Solve this true/flase linear algebra question. Please show your work.

**Null Space of a Matrix** Given the following matrix \( A \) and vector \( \mathbf{w} \): \[ A = \begin{bmatrix} -8 & -2 & -9 \\ 6 & 4 & 8 \\ 4 & 0 & 4 \end{bmatrix} \quad \text{and} \quad \mathbf{w} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix} \] Is it true that \( \mathbf{w} \) is in the Null Space of \( A \) (Null(A))? **Options:** - True - False **Explanation:** To determine if \( \mathbf{w} \) is in the Null Space of \( A \), we need to verify if the matrix-vector product \( A\mathbf{w} \) results in the zero vector. In other words, we need to check if: \[ A\mathbf{w} = \mathbf{0} \] Perform the matrix multiplication \( A\mathbf{w} \) to find out. If the result is the zero vector, then \( \mathbf{w} \) is in the Null Space of \( A \); otherwise, it is not.
Transcribed Image Text:**Null Space of a Matrix** Given the following matrix \( A \) and vector \( \mathbf{w} \): \[ A = \begin{bmatrix} -8 & -2 & -9 \\ 6 & 4 & 8 \\ 4 & 0 & 4 \end{bmatrix} \quad \text{and} \quad \mathbf{w} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix} \] Is it true that \( \mathbf{w} \) is in the Null Space of \( A \) (Null(A))? **Options:** - True - False **Explanation:** To determine if \( \mathbf{w} \) is in the Null Space of \( A \), we need to verify if the matrix-vector product \( A\mathbf{w} \) results in the zero vector. In other words, we need to check if: \[ A\mathbf{w} = \mathbf{0} \] Perform the matrix multiplication \( A\mathbf{w} \) to find out. If the result is the zero vector, then \( \mathbf{w} \) is in the Null Space of \( A \); otherwise, it is not.
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