To Submit 1. Exercise 2.1.15(c) Determine the matrix A if (2A−3 [1_2_0])² =3A²+ [2_1 −1]”. 1 4 2. Let A = 1 -3 4 -2 -1 3 0 -1 3 |, y = 4. Let A = 1 0 -3 (a) Can you express y as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, 2 and 23 such that y = £₁ª₁ + x2ª₂ +23a3 or explain why they don't exist. and z = (b) Can you express z as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x₁, 2 and 23 such that z = £₁ª₁ + x2ª2 +£3a3 or explain why they don't exist. (c) Determine all the vectors in R³ that are linear combinations of the columns of A, that is what conditions b1 b2 can be written as a linear combination of a₁, a2, a3. b3 3. Exercise 2.3.8.c. Given an example of A and B, both 2 × 2 matrices such that AB = 0 but BA ‡ 0. 0 2 2 (the 2 x 2 identity matrix). must we put on b₁,b2, b3 such that b = and I = (a) Can you find a 2 x 2 matrix B with AB = I? Give a specific matrix B or explain why it can not exist. (b) Can you find a 2 × 2 matrix B with CB = I? Give a specific matrix B or explain why it can not exist.
To Submit 1. Exercise 2.1.15(c) Determine the matrix A if (2A−3 [1_2_0])² =3A²+ [2_1 −1]”. 1 4 2. Let A = 1 -3 4 -2 -1 3 0 -1 3 |, y = 4. Let A = 1 0 -3 (a) Can you express y as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, 2 and 23 such that y = £₁ª₁ + x2ª₂ +23a3 or explain why they don't exist. and z = (b) Can you express z as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x₁, 2 and 23 such that z = £₁ª₁ + x2ª2 +£3a3 or explain why they don't exist. (c) Determine all the vectors in R³ that are linear combinations of the columns of A, that is what conditions b1 b2 can be written as a linear combination of a₁, a2, a3. b3 3. Exercise 2.3.8.c. Given an example of A and B, both 2 × 2 matrices such that AB = 0 but BA ‡ 0. 0 2 2 (the 2 x 2 identity matrix). must we put on b₁,b2, b3 such that b = and I = (a) Can you find a 2 x 2 matrix B with AB = I? Give a specific matrix B or explain why it can not exist. (b) Can you find a 2 × 2 matrix B with CB = I? Give a specific matrix B or explain why it can not exist.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![To Submit
1. Exercise 2.1.15(c) Determine the matrix A if (2A −3 [1_2_0])¹ = 3A² + [2_1 −1]".
-----0
, у
3
2. Let A =
1 -2
-3 3
4. Let A =
4
1
and z =
(a) Can you express y as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, x2 and
x3 such that y = £₁ª₁ + x2ª₂ + x3a3 or explain why they don't exist.
1
(b) Can you express z as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, x2 and
x3 such that z = X1ª₁ + X2ª2 +£3ª3 or explain why they don't exist.
(c) Determine all the vectors in R³ that are linear combinations of the columns of A, that is what conditions
b₁
must we put on b₁,b2, b3 such that b = b2 can be written as a linear combination of a₁, a2, a3.
|b3|
3. Exercise 2.3.8.c. Given an example of A and B, both 2 × 2 matrices such that AB = 0 but BA ‡ 0.
1
0
(2), 0 = [22]
C
BA
(the 2 × 2 identity matrix).
and I =
(a) Can you find a 2 × 2 matrix B with AB = I? Give a specific matrix B or explain why it can not exist.
(b) Can you find a 2 × 2 matrix B with CB = I? Give a specific matrix B or explain why it can not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40baf6ed-86bf-41a4-92b1-81bfc40321fa%2F544cb1e2-a96d-486b-88ad-2466ec6601e0%2Fh9bv8an_processed.png&w=3840&q=75)
Transcribed Image Text:To Submit
1. Exercise 2.1.15(c) Determine the matrix A if (2A −3 [1_2_0])¹ = 3A² + [2_1 −1]".
-----0
, у
3
2. Let A =
1 -2
-3 3
4. Let A =
4
1
and z =
(a) Can you express y as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, x2 and
x3 such that y = £₁ª₁ + x2ª₂ + x3a3 or explain why they don't exist.
1
(b) Can you express z as a linear combination of the columns of A, a₁, a2 and a3? Either find specific x1, x2 and
x3 such that z = X1ª₁ + X2ª2 +£3ª3 or explain why they don't exist.
(c) Determine all the vectors in R³ that are linear combinations of the columns of A, that is what conditions
b₁
must we put on b₁,b2, b3 such that b = b2 can be written as a linear combination of a₁, a2, a3.
|b3|
3. Exercise 2.3.8.c. Given an example of A and B, both 2 × 2 matrices such that AB = 0 but BA ‡ 0.
1
0
(2), 0 = [22]
C
BA
(the 2 × 2 identity matrix).
and I =
(a) Can you find a 2 × 2 matrix B with AB = I? Give a specific matrix B or explain why it can not exist.
(b) Can you find a 2 × 2 matrix B with CB = I? Give a specific matrix B or explain why it can not exist.
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