6 11 points previous answers holtlinalg1 32016 expand

A = A
2
A
2
= = .
−2 9
0 5
−2 9
0 5
4 27
0 25
6. 1/1 points | Previous Answers HoltLinAlg1 3.2.016.
Expand the given matrix expression and combine as many terms as possible. Assume that all
matrices are
Solution or Explanation
n
×
n .
( A + I )( A
2
+ A
( A + I )( A
2
+ A ) = A ( A
2
+ A ) + I ( A
2
+ A ) = A ( A
2
) + A ( A ) + ( A
2
+ A ) = A
3
+ A
2
+ A
+ 2 A
2
+
)
2
+ A = A
3
A

2015 年 3 月 17 日 UW Common Math 308 Section 3.2
7. 1/1 points | Previous Answers HoltLinAlg1 3.2.019.
The given matrix equation is not true in general. Explain why. Assume that all matrices are
n
×
n .
( A + B )
2
= A
2
+ 2 AB +
( A + B )
2
= A
2
+ AB + BA + B
2
. This is only equal to A
2
+ 2 AB + B
2
when AB
which in general is not true.
( A + B )
2
= A
2
+ AB + BA + B
2
. This is only equal to A
2
+ 2 AB + B
2
when AB
which in general is not true.
( A + B )
2
= A
2
+ AB − AB + B
2
= A
2
+ B
2
. This is only equal to A
2
+ 2 AB + B
= 0
nn
or B = 0
nn
, which in general is not true.
( A + B )
2
= A
2
− BA + BA + B
2
= A
2
+ B
2
. This is only equal to A
2
+ 2 AB + B
= 0
nn
or B = 0
nn
, which in general is not true.
B
2
= BA ,
= − BA ,
2
when A
2
when A
BA + B
2
.
,
6/9

2015 年 3 月 17 日 UW Common Math 308 Section 3.2
8. 1/1 points | Previous Answers HoltLinAlg1 3.2.031.
Find an example that meets the given specifications.
3
×
3 matrices A and B such that
1 2 3
4 5 6
7 8 9
[0, 0, 0; 0, 0, 0; 0, 0, 1]
For example, Then and
9. 1/1 points | Previous Answers HoltLinAlg1 3.2.034.
Find an example that meets the given specifications.