Consider the following matrix: A3 = 1011 0 0 0 a22 0 0 0 433. .) In this part (only), suppose that the matrix A is idempotent and invertible. In this case, will the left-hand side of the following equation equal the right-hand side? [(A x A' × A' × A × {A-¹}³ × A)-¯¹]' = (A¹)¯¹ Show all necessary calculations. ) Suppose: Ak = AX AX AX AX ...x A. Under what conditions will A2,500 = k times calculations or provide a brief explanation. :) Do the conditions in part (b) guarantee that A is invertible? ) Derive A-¹ and state the conditions for A to be invertible. Show all necessary calculations. A300? Show all necessary
Consider the following matrix: A3 = 1011 0 0 0 a22 0 0 0 433. .) In this part (only), suppose that the matrix A is idempotent and invertible. In this case, will the left-hand side of the following equation equal the right-hand side? [(A x A' × A' × A × {A-¹}³ × A)-¯¹]' = (A¹)¯¹ Show all necessary calculations. ) Suppose: Ak = AX AX AX AX ...x A. Under what conditions will A2,500 = k times calculations or provide a brief explanation. :) Do the conditions in part (b) guarantee that A is invertible? ) Derive A-¹ and state the conditions for A to be invertible. Show all necessary calculations. A300? Show all necessary
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 70E
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![Please teach how to solve not just solve (concepts)
Consider the following matrix:
A3 =
1a11
0
0
0
0
a22 0
0 a33/
·)
In this part (only), suppose that the matrix A is idempotent and invertible. In this case, will the left-hand side of
the following equation equal the right-hand side?
[(A x A' x A' x A × {A-¹}³ × A)¯¹]' = (A¹)-¹
Show all necessary calculations.
) Suppose: Ak = AX AX AX AX ...x A. Under what conditions will A2,500 = A300? Show all necessary
k times
calculations or provide a brief explanation.
:) Do the conditions in part (b) guarantee that A is invertible?...
) Derive A-¹ and state the conditions for A to be invertible. Show all necessary calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F898cbd98-1de8-493f-9103-82a631e26b34%2Fb00b9dd9-99cc-40b9-950a-020d130bfb10%2Fr42fr5q_processed.png&w=3840&q=75)
Transcribed Image Text:Please teach how to solve not just solve (concepts)
Consider the following matrix:
A3 =
1a11
0
0
0
0
a22 0
0 a33/
·)
In this part (only), suppose that the matrix A is idempotent and invertible. In this case, will the left-hand side of
the following equation equal the right-hand side?
[(A x A' x A' x A × {A-¹}³ × A)¯¹]' = (A¹)-¹
Show all necessary calculations.
) Suppose: Ak = AX AX AX AX ...x A. Under what conditions will A2,500 = A300? Show all necessary
k times
calculations or provide a brief explanation.
:) Do the conditions in part (b) guarantee that A is invertible?...
) Derive A-¹ and state the conditions for A to be invertible. Show all necessary calculations.
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