3. Is the matrix 5 psd, pd, nsd, nd, or indefinite? Justify your answer.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section6.2: The Algebra Of Matrices
Problem 61E
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Question
1. Consider the matrices
-2
- (1), 42-(3-2) ₁4 = ( −² −2).
A3
1
3
Explain briefly.
2. Consider matrices of the form
These matrices can be used to build functions at A₁, 2¹ A₂, A3z, and 2¹A4. These functions
are represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture.
(a) Mas 20.
(b) Ma, 30.
0
3. Is the matrix
(b)
(c)
Figure 1: Graphical representation of functions
Ma,8: a
₂ ( -12-22)
²2 ) + ³ ( − ¹ − 1 )
and A4 =
-(-6).
-4
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
5 -1
-1 4
psd, pd, nsd, nd, or indefinite? Justify your answer.
(d)
Transcribed Image Text:1. Consider the matrices -2 - (1), 42-(3-2) ₁4 = ( −² −2). A3 1 3 Explain briefly. 2. Consider matrices of the form These matrices can be used to build functions at A₁, 2¹ A₂, A3z, and 2¹A4. These functions are represented (in an arbitrary order) in Figure 1. Match each matrix with its corresponding picture. (a) Mas 20. (b) Ma, 30. 0 3. Is the matrix (b) (c) Figure 1: Graphical representation of functions Ma,8: a ₂ ( -12-22) ²2 ) + ³ ( − ¹ − 1 ) and A4 = -(-6). -4 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 5 -1 -1 4 psd, pd, nsd, nd, or indefinite? Justify your answer. (d)
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