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Calculate the /,1,1 norms of the following vectors: 1 2 00 a = For a) 1₁ = 1 32 For d) || 2 12 = , 12 = ∞

Calculate the /,1,1 norms of the following vectors: 1 2 00 a = For a) 1₁ = 1 32 For d) || 2 12 = , 12 = ∞

Algebra and Trigonometry (6th Edition)
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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**Instruction: Calculate the \( l_1, l_2, l_\infty \) norms of the following vectors:** \[ a = \begin{pmatrix} 1 \\ 3 \\ 2 \end{pmatrix}, \quad d = \begin{pmatrix} 2 \\ -2 \\ 1 \end{pmatrix} \] **For vector \( a \):** - \( l_1 = \) [Input box] - \( l_2 = \) [Input box] - \( l_\infty = \) [Input box] **For vector \( d \):** - \( l_1 = \) [Input box] - \( l_2 = \) [Input box] - \( l_\infty = \) [Input box] **Explanation of Norms:** - The \( l_1 \) norm of a vector is the sum of the absolute values of its components. - The \( l_2 \) norm, or Euclidean norm, is the square root of the sum of the squares of its components. - The \( l_\infty \) norm is the maximum absolute value of its components.
Transcribed Image Text:**Instruction: Calculate the \( l_1, l_2, l_\infty \) norms of the following vectors:** \[ a = \begin{pmatrix} 1 \\ 3 \\ 2 \end{pmatrix}, \quad d = \begin{pmatrix} 2 \\ -2 \\ 1 \end{pmatrix} \] **For vector \( a \):** - \( l_1 = \) [Input box] - \( l_2 = \) [Input box] - \( l_\infty = \) [Input box] **For vector \( d \):** - \( l_1 = \) [Input box] - \( l_2 = \) [Input box] - \( l_\infty = \) [Input box] **Explanation of Norms:** - The \( l_1 \) norm of a vector is the sum of the absolute values of its components. - The \( l_2 \) norm, or Euclidean norm, is the square root of the sum of the squares of its components. - The \( l_\infty \) norm is the maximum absolute value of its components.
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