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2. Consider matrices of the form -2 1 = a ( - 1² - ²2² ) + ³ ( -7 _ ²2 ) B B -2 1 -2 (a) Ma,B≥ 0. (b) Maß ≤ 0. Ma,B := a where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, or indefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix

2. Consider matrices of the form -2 1 = a ( - 1² - ²2² ) + ³ ( -7 _ ²2 ) B B -2 1 -2 (a) Ma,B≥ 0. (b) Maß ≤ 0. Ma,B := a where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, or indefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 6E
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Please answer question 2

1. Consider the matrices 4 A₁ = -(13) 42-(3-2) 0 23-2). These matrices can be used to build functions x¹A₁x, x¹ A₂x, x¹ A3x, and x¹ A4x. These functions are represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture. = Explain briefly. 2. Consider matrices of the form (a) Ma, ≥ 0. (b) Ma,ß ≤ 0. 3. Is the matrix Ma,8:= a 0 (b) (c) Figure 1: Graphical representation of functions , A3 = 1 -a 0 0 1 -2 α ( -2 -² ) + ³ ( -1 -₂ ) 2 -2 where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, or indefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix 5 -4 1 psd, pd, nsd, nd, or indefinite? Justify your answer. 4. Consider the matrix " 1 5 -1 4 and A4 = -5 -4 0 0 -a 0 -2a (a² + a) 0 - (2-a²) (2-a²) (2-a²) 2+ 4a - a² -2a Find all values of a for which this matrix is psd. Are there values of a for which the matrix is pd? ə
Transcribed Image Text:1. Consider the matrices 4 A₁ = -(13) 42-(3-2) 0 23-2). These matrices can be used to build functions x¹A₁x, x¹ A₂x, x¹ A3x, and x¹ A4x. These functions are represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture. = Explain briefly. 2. Consider matrices of the form (a) Ma, ≥ 0. (b) Ma,ß ≤ 0. 3. Is the matrix Ma,8:= a 0 (b) (c) Figure 1: Graphical representation of functions , A3 = 1 -a 0 0 1 -2 α ( -2 -² ) + ³ ( -1 -₂ ) 2 -2 where a and 3 are scalars. Depending on the values of a and 3, these matrices might be psd, nsd, or indefinite. In a graph with axes a and 3, represent the set of all (a, 3) values for which the matrix 5 -4 1 psd, pd, nsd, nd, or indefinite? Justify your answer. 4. Consider the matrix " 1 5 -1 4 and A4 = -5 -4 0 0 -a 0 -2a (a² + a) 0 - (2-a²) (2-a²) (2-a²) 2+ 4a - a² -2a Find all values of a for which this matrix is psd. Are there values of a for which the matrix is pd? ə
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