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Probability helps us to know the chances of an event occurring. The correct option is A.
<h3>What is Probability?</h3>Probability helps us to know the chances of an event occurring.
Dependent events are those events in which the outcome of the first event affects the outcome of the second event. The statement that is correct about the dependent event is that the probability of all dependent events can be calculated using the "OR" formula P(A+B) =P(A) +P(B)-P(A and B).
Hence, the correct option is A.
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Since the multiplication between two matrices is not <em>commutative</em>, then , regardless of the dimensions of
.
<h3>Is the product of two matrices commutative?</h3>
In linear algebra, we define the product of two matrices as follows:
, where
,
and
(1)
Where each element of the matrix is equal to the following dot product:
, where 1 ≤ i ≤ m and 1 ≤ j ≤ n. (2)
Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not <em>commutative</em> because of the nature and characteristics of the definition itself, which implies operating on a row of the <em>former</em> matrix and a column of the <em>latter</em> matrix.
Such <em>"arbitrariness"</em> means that <em>resulting</em> value for will be different if the order between
and
is changed and even the dimensions of
may be different. Therefore, the proposition is false.
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