For a given matrix A = , the matrix P that is diagonalizes A is () P = [{ 4] «#) P = [ )A. None of the given answers is true )B. only (i) is true )C. only (ii) is true D. only (iii) is true

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please help me with both number 1 and 2

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2
For a given matrix A =
the matrix P that is diagonalizes A is
-2 1
1
1
(ii) P =
-1
(i) P =
(iii) P =
-1
A. None of the given answers is true
B. only (i) is true
C. only (ii) is true
D. only (iii) is true
1.
Suppose T : R³ → R³ is linear and has an upper-triangular matrix with respect
to the basis (1, 1, 1), (0, 2, 2), (0, 1, 2). Then, the orthonormal basis of R³ with
respect to which T has an upper-triangular matrix is
(1) ( ) t) (0, -
(2) ( )( (1,0, 0)
(3) ( )(- , (0, –)
A. only (2) is true
B. only (3) is true
C. None of the given answers is true
all
2.
D. only (1) is true
04:16 PM
2021-10-25
Page: 1 of 1
Words: 2
E EI E E 96% e
Transcribed Image Text:Document7 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? A Find - A % Cut - 11 * A A Aa =、三, 幸 刻T Calibri (Body) E Copy AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB[ AaBbCcl ae Replace Paste в IUabe X, х* I No Spaci. Heading 1 Change Styles I Normal Heading 2 Title Subtitle A Select - Format Painter Clipboard Font Paragraph Styles Editing L 2.1 1·L:X::1:L·2:1·3 4: 1 5.1 6.1 7:18: 1 • 9. L'10. 11:1 12·I 13. 1 14 L 15. 1 ' 17. 1 18. 2 For a given matrix A = the matrix P that is diagonalizes A is -2 1 1 1 (ii) P = -1 (i) P = (iii) P = -1 A. None of the given answers is true B. only (i) is true C. only (ii) is true D. only (iii) is true 1. Suppose T : R³ → R³ is linear and has an upper-triangular matrix with respect to the basis (1, 1, 1), (0, 2, 2), (0, 1, 2). Then, the orthonormal basis of R³ with respect to which T has an upper-triangular matrix is (1) ( ) t) (0, - (2) ( )( (1,0, 0) (3) ( )(- , (0, –) A. only (2) is true B. only (3) is true C. None of the given answers is true all 2. D. only (1) is true 04:16 PM 2021-10-25 Page: 1 of 1 Words: 2 E EI E E 96% e
Expert Solution
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“Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question”

A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a matrix is defined as m×n, where m is the number of rows and n is the number of columns.

If the number of rows of a matrix is equal to its number of columns, then it is called a square matrix. If the main diagonal elements of a square matrix are equal to 1 and all others are equal to zero, then it is called an identity matrix.

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