please answer the questions 18,19 and 31 please and also please write it in a white paper38
Chapter 1 Systems of Linear Equations and Matrices
In Exercises 13-16, use the matrices
:] – [ -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
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
28. Let A = Find all matrices of the form
such that AM = MA
29. Find matrices A and B such that AB = 0 but
30. Show there are no 2 x 2 matrices A and B such
AB – BA
Whenever possible, perform the operations. If a
computation cannot be made, explain why.
17. 2A – B
B! – 2A
Determine all values of a and b such that
12 3 b -5 6
21. (A + B)
22. C(A’ + B’)
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.
A=0 -1 0
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.
= [ _}]
-=[ 7 ]
Show that AB = AC and yet B #C.
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