In Exercises 1 and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2 A = 0 -1 4 -5 = -5 -4 - [² -[-2 1] D-[-2 = ] - -3]. $) *=[3] 3 c = C E 1. -2A, B-2A, AC, CD -2). B
In Exercises 1 and 2, compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let 2 A = 0 -1 4 -5 = -5 -4 - [² -[-2 1] D-[-2 = ] - -3]. $) *=[3] 3 c = C E 1. -2A, B-2A, AC, CD -2). B
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
1
![2 0
A = [² -3 -2]
4 -5
c = [|
2.1
EXERCISES
In Exercises I and 2, compute each matrix sum or product if it is
defined. If an expression is undefined, explain why. Let
2].
1. -2A, B - 2A, AC, CD
1
-2
A =
3. Let A =
-[-
1
B = [1 ]
-4 -3
3
-1
D =
4
=[$ =2]. Compute
5
-2
2. Let A be a 4 x 4 matrix and let x be a vector in R4. What is the fastest way to compute
A²x? Count the multiplications.
-2 4]
T
Compute (Ax), xTAT, xx", and xTx. Is ATx" defined?
9
3. Suppose A is an m x n matrix, all of whose rows are identical. Suppose B is an n x p
matrix, all of whose columns are identical. What can be said about the entries in AB
FLAATIO
-5
2. A + 2B, 3C - E, CB, EB
In the rest of this exercise set and in those to follow, you should
assume that each matrix expression is defined. That is, the sizes
of the matrices (and vectors) involved "match" appropriately.
5
$]. E = [3]
4
4 Compute A-513 and (513) A, when
9 -1 3
-8 7 -6
-4 1 8
Compute 312 - A and (31₂) A.
In Exercises 5 and 6, compute the product AB in two ways: (a) by
the definition, where Ab, and Ab2 are computed separately, and
(b) by the row-column rule for computing AB.
5. A =
=
COMUN
5
2
4
-3
-2
0
6.
A 3 5
2
4
-3
10. Let A
, B =
H
11. Let A =
=
3-2
-2
© M3R03H1
7. If a matrix A is 5 × 3 and the product AB is 5 x 7, what is the
size of B?
2 -3
· B = [ ²2
- [23]
8. How many rows does B have if BC is a 3 x 4 matrix?
2
5
V [ - ] and B = [₁ ]
Let A
4 -5
3 k
-3
1
k, if any, will make AB = BA?
=
-[-
³ ] ₁ B = [ $
$].
5
5
-4
Verify that AB = AC and yet BC.
8 4
13] 20
5
and D= =
What value(s) of
[2
and C =
- [5
3
- 1
0
0
030 0. Com-
005
1
1
2
1
4
pute AD and DA. Explain how the columns or rows of A
change when A is multiplied by D on the right or on the
left. Find a 3 x 3 matrix B, not the identity matrix or the zero
matrix, such that AB = BA.
Exerci
which the ir
statement Tr
15. a.
If A
res
b. Eac
of
C.
d.
e.
16./a.
A
b.
A
ΤΙ
C.
d.
O
e.
If
17. If
th
18. Su
M
W
V
19. S
20.
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12f186d1-b037-4d7e-ab2f-58fa2244e958%2F1a0b03d4-3b86-45f4-b50a-bda278ad7522%2F08gdwn8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2 0
A = [² -3 -2]
4 -5
c = [|
2.1
EXERCISES
In Exercises I and 2, compute each matrix sum or product if it is
defined. If an expression is undefined, explain why. Let
2].
1. -2A, B - 2A, AC, CD
1
-2
A =
3. Let A =
-[-
1
B = [1 ]
-4 -3
3
-1
D =
4
=[$ =2]. Compute
5
-2
2. Let A be a 4 x 4 matrix and let x be a vector in R4. What is the fastest way to compute
A²x? Count the multiplications.
-2 4]
T
Compute (Ax), xTAT, xx", and xTx. Is ATx" defined?
9
3. Suppose A is an m x n matrix, all of whose rows are identical. Suppose B is an n x p
matrix, all of whose columns are identical. What can be said about the entries in AB
FLAATIO
-5
2. A + 2B, 3C - E, CB, EB
In the rest of this exercise set and in those to follow, you should
assume that each matrix expression is defined. That is, the sizes
of the matrices (and vectors) involved "match" appropriately.
5
$]. E = [3]
4
4 Compute A-513 and (513) A, when
9 -1 3
-8 7 -6
-4 1 8
Compute 312 - A and (31₂) A.
In Exercises 5 and 6, compute the product AB in two ways: (a) by
the definition, where Ab, and Ab2 are computed separately, and
(b) by the row-column rule for computing AB.
5. A =
=
COMUN
5
2
4
-3
-2
0
6.
A 3 5
2
4
-3
10. Let A
, B =
H
11. Let A =
=
3-2
-2
© M3R03H1
7. If a matrix A is 5 × 3 and the product AB is 5 x 7, what is the
size of B?
2 -3
· B = [ ²2
- [23]
8. How many rows does B have if BC is a 3 x 4 matrix?
2
5
V [ - ] and B = [₁ ]
Let A
4 -5
3 k
-3
1
k, if any, will make AB = BA?
=
-[-
³ ] ₁ B = [ $
$].
5
5
-4
Verify that AB = AC and yet BC.
8 4
13] 20
5
and D= =
What value(s) of
[2
and C =
- [5
3
- 1
0
0
030 0. Com-
005
1
1
2
1
4
pute AD and DA. Explain how the columns or rows of A
change when A is multiplied by D on the right or on the
left. Find a 3 x 3 matrix B, not the identity matrix or the zero
matrix, such that AB = BA.
Exerci
which the ir
statement Tr
15. a.
If A
res
b. Eac
of
C.
d.
e.
16./a.
A
b.
A
ΤΙ
C.
d.
O
e.
If
17. If
th
18. Su
M
W
V
19. S
20.
20
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