1. Let A= - [²3]. Find A², A-¹, (4-1) and (47)-1,
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 32E
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Kindly solve Q1 ASAP and get the thumbs up please show me neat and clean work for it by hand solution needed
![1. Let A =
2. Let A=
2 1
Find AT, A¹, (A-¹) and (4¹)-¹
-[3
6. Let A=
and B =
22
(a) Find (AB), BT AT and ATBT
(b) (AB)¹, B¹A¹ and A¹B¹
3. By trial and error, find a 2 x 2 nonzero matrix A such that A² = 0.
4. Prove or disprove that the following sets are subspaces of R².
21
) $₁ = (x = [ ²1 ] * such that r₁= 5₂).
22
(b) S₂ = (x = [2
such that z 20.72₂ 20).
22
(c) S₁ = (2=[22] such that zį = 22 +1}.
5. Prove or disprove that the following sets are subspaces of the space of 2 x 2 matrices.
(a) S₁ is the set of 2 x 2 matrices A such that: 412021 and 110220
(b) S₂ is the set of 2 x 2 matrices A such that: 0₁1-022=0.
(c) S₁ is the set of singular (non-invertible) 2 x 2 matrices
1 01-2
12-1 2
1-2 0
0
-2-3 2 0
and let b
a
(a) Find the rref(A).
(b) Find the rank of A.
(e) Find a such that b is in the column space of A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cb50e1b-92d6-4e56-8b1a-bccd4202bf82%2F4aa273f1-a5c5-4f8e-aad3-570ebdbd18d7%2Fwqps5wp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let A =
2. Let A=
2 1
Find AT, A¹, (A-¹) and (4¹)-¹
-[3
6. Let A=
and B =
22
(a) Find (AB), BT AT and ATBT
(b) (AB)¹, B¹A¹ and A¹B¹
3. By trial and error, find a 2 x 2 nonzero matrix A such that A² = 0.
4. Prove or disprove that the following sets are subspaces of R².
21
) $₁ = (x = [ ²1 ] * such that r₁= 5₂).
22
(b) S₂ = (x = [2
such that z 20.72₂ 20).
22
(c) S₁ = (2=[22] such that zį = 22 +1}.
5. Prove or disprove that the following sets are subspaces of the space of 2 x 2 matrices.
(a) S₁ is the set of 2 x 2 matrices A such that: 412021 and 110220
(b) S₂ is the set of 2 x 2 matrices A such that: 0₁1-022=0.
(c) S₁ is the set of singular (non-invertible) 2 x 2 matrices
1 01-2
12-1 2
1-2 0
0
-2-3 2 0
and let b
a
(a) Find the rref(A).
(b) Find the rank of A.
(e) Find a such that b is in the column space of A.
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