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Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.) [ 2 -1 A = -4 2

Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.) [ 2 -1 A = -4 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.) \[ A = \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix} \] **Visual Explanation:** Below the matrix, a diagram is depicted showing a transformation of a bracketed vector. The diagram includes: - **Left Bracket:** Represents the input vector. - **Middle Matrix Placeholder:** Two blank spaces indicating a vector with two elements; an arrow pointing right signifies a mapping through matrix multiplication. - **Right Bracket:** Represents the resulting vector. - **Arrows:** - Green arrow pointing downwards on the left, suggesting initial entry or importance. - Gray arrow between the two sides of the vector notation, symbolizing the action of the matrix on the vector. **Guideline:** Enter the basis vectors for the nullspace in the given spaces. If there is no basis, type "NONE" in a single cell.
Transcribed Image Text:**Problem Statement:** Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.) \[ A = \begin{bmatrix} 2 & -1 \\ -4 & 2 \end{bmatrix} \] **Visual Explanation:** Below the matrix, a diagram is depicted showing a transformation of a bracketed vector. The diagram includes: - **Left Bracket:** Represents the input vector. - **Middle Matrix Placeholder:** Two blank spaces indicating a vector with two elements; an arrow pointing right signifies a mapping through matrix multiplication. - **Right Bracket:** Represents the resulting vector. - **Arrows:** - Green arrow pointing downwards on the left, suggesting initial entry or importance. - Gray arrow between the two sides of the vector notation, symbolizing the action of the matrix on the vector. **Guideline:** Enter the basis vectors for the nullspace in the given spaces. If there is no basis, type "NONE" in a single cell.
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