Select Page

Chapter 1 Systems of Linear Equations and Matrices
In Exercises 13-16, use the matrices
A=
-2-3
BE
20
0
3
0
:] – [ -3
c=[ – -:]
Find a 2 x 2 matrix B that is not the zero matrix,
such that AB is the zero matrix.
27. Find all 2 x 2 matrices of the form
a b
0
such that
10
A² = AA = -[6 :]
13. Find A(B+C).
14. Find (A + B)C.
15. Find 2A(B-3C).
16. Find (A + 2B)(3C).
In Exercises 17-24, use the matrices
2 0-1
A=
10-2
28. Let A = Find all matrices of the form
ab
M
such that AM = MA
cd
29. Find matrices A and B such that AB = 0 but
BA+0.
30. Show there are no 2 x 2 matrices A and B such
that
AB – BA
BE
-3
-3
1
-3
-]
c=[ –
-1
BA=[6 i]
-1
Whenever possible, perform the operations. If a
computation cannot be made, explain why.
17. 2A – B
B! – 2A
19. AB
Determine all values of a and b such that
12 3 b -5 6
12 16
20. BA’
0
21. (A + B)
22. C(A’ + B’)
23. (AC)B
24. (ABC
25. Let
32. If A and B are 2 x 2 matrices, show that the sum
of the terms on the diagonal of AB – BA is 0.
33. Let
1
001
A=0 -1 0
0 1
Find the matrix A20
34. If A and B are n x n matrices, when does
(A + B)(A – B) = A2-B2?
35. If the matrices A and B commute, show that
A B = BA?
36. Suppose A, B, and are n x n matrices and B
and C both commute with A.
a. Show that BC and A commute,
b. Give specific matrices to show that BC and
CB do not have to be equal.
B=
= [ _}]
-=[ 7 ]
c=[-
7 5
– 2
Show that AB = AC and yet B #C.
26. Let
02
A =
0 5
= [

attachment

#### Why Choose Us

• 100% non-plagiarized Papers
• Affordable Prices
• Any Paper, Urgency, and Subject
• Will complete your papers in 6 hours
• On-time Delivery
• Money-back and Privacy guarantees
• Unlimited Amendments upon request
• Satisfaction guarantee

#### How it Works

• Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
• Fill in your paper’s requirements in the "PAPER DETAILS" section.