The inclusion/exclusion principle states that
That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).
Therefore,
will have the most elements when the sets
and
are disjoint, i.e.
, which would mean the most we can can in this case would be
(Note that
denotes the cardinality of the set
.)
Answer:
∠ e = 40°
Step-by-step explanation:
Since Δ ABC and Δ EDC are congruent then corresponding angles are congruent, that is
∠ A = ∠ E = 40°
Answer:-7d=13
7d=-13
d=-13/7
Step-by-step explanation:
Hope this helps!
Make sure to apply same operations to both sides.
Answer:
32/9
Step-by-step explanation:
2 to the fifth power is 32. 3 to the second power is 9.
A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).
b. True. Suppose
is the matrix of the eigenvectors of
, and
is the diagonal matrix of the eigenvalues of
:
Then
In other words, the columns of
are
, which are identically
, and these are the columns of
.
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue
and eigenvector
, where
. But the matrix can't be diagonalized.
