Seven ping-pong balls numbered 1-7 are put in a hat. Three balls are chosen without replacement. What is the probability that al
2 answers:
<h2>Answer:</h2>
The probability that all three numbers are even numbers is:
There are seven balls numbered as: 1-7
and the number of even numbers are: 3 ( i.e. 2,4 and 6 )
Three balls are chosen without replacement.
Hence, the probability that all three numbers are even numbers is given by:
Ratio of number of favorable outcomes to the total number of outcomes.
Hence, the probability is:
where the numerator represents that the balls drawn have even numbers.
and the denominator denote the choosing of 3 balls out of a total of 7 balls.
Hence, the probability is:
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Answer:
Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.
Step-by-step explanation:
Given A is an matrix. Let
be the corresponding linear transformationover the field F and
be identity vector in V. Now if
.
(1) The kernel of a linear transformation is a vector space : True.
Let , then,
hence the kernel is closed under addition.
Let , then
and thus Ket(T) is closed under multiplication
Finally, fore all vectors ,
Thus Ker(T) is a subspace.
(2) If the equation Ax=b is consistent, then Col(A) is : False
if the equation Ax=b is consistent, then Col(A) must be consistent for all b.
(3) The null space of an mxn matrix is in
: False
The null space that is dimension of solution space of an m x n matrix is always in .
(4) The column space of A is the range of the mapping
: True.
(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.
Here Ax will give a linear combination of column of A as a weights of x.
(6) The null space of A is the solution set of the equation Ax=0.
: True