Problem #4: Let Problem #4(b): A = |-1 (A) (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = PAP using the (correct) answer from (a). Enter the diagonal entries of B, in order, into the answer box below. i.e.. enter b11. 622, 633 (in that order). ⑤ V2 0 ㅎㅎ 0 Problem #4(a): Select V -1 4 -1 -1 4 옳 살 V3 (B) 0 하 V3 Vo 0 19 물 12 F 4² 4² 42 -| (C) (G) 수 V2 0 4² 42 42 12 42 2 용 하 옳옳 (D) V2 (H) 0 V2 0 4 4 4 V3 4 2 V3 하하하
Problem #4: Let Problem #4(b): A = |-1 (A) (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = PAP using the (correct) answer from (a). Enter the diagonal entries of B, in order, into the answer box below. i.e.. enter b11. 622, 633 (in that order). ⑤ V2 0 ㅎㅎ 0 Problem #4(a): Select V -1 4 -1 -1 4 옳 살 V3 (B) 0 하 V3 Vo 0 19 물 12 F 4² 4² 42 -| (C) (G) 수 V2 0 4² 42 42 12 42 2 용 하 옳옳 (D) V2 (H) 0 V2 0 4 4 4 V3 4 2 V3 하하하
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.1: Algebra Of 2 X 2 Matrices
Problem 46PS
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Step 1: Define orgthogonal diagoalnalization
VIEWStep 2: Determine the eigenvalues of A
VIEWStep 3: Determine the corresponding eigenvector for the eigenvalue 2
VIEWStep 4: Determine the corresponding eigenvectors for the eigenvalue 5
VIEWStep 5: Determine the corresponding orthogonal eigenvectors
VIEWStep 6: Normalise the eigenvectors
VIEWStep 7: Take an orthogonal matrix P
VIEWStep 8: Determine B
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