Let G be the set of all matrices in M 3 ( ℝ ) that have the form [ a 0 0 0 b 0 0 0 c ] with all three numbers a , b , and c nonzero. Prove or disprove that G is a group with respect to multiplication.
Let G be the set of all matrices in M 3 ( ℝ ) that have the form [ a 0 0 0 b 0 0 0 c ] with all three numbers a , b , and c nonzero. Prove or disprove that G is a group with respect to multiplication.
Solution Summary: The author explains that the set G of all matrices in M_3(R) with all three numbers is a group with respect to multiplication.
Evaluate the following expression and show your work to support your calculations.
a). 6!
b).
4!
3!0!
7!
c).
5!2!
d). 5!2!
e).
n!
(n - 1)!
Amy and Samiha have a hat that contains two playing cards, one ace and one king. They are playing a game where they randomly pick a card out of the hat four times, with replacement.
Amy thinks that the probability of getting exactly two aces in four picks is equal to the probability of not getting exactly two aces in four picks. Samiha disagrees. She thinks that the probability of not getting exactly two aces is greater.
The sample space of possible outcomes is listed below. A represents an ace, and K represents a king. Who is correct?
Consider the exponential function f(x) = 12x. Complete the sentences about the key features of the graph.
The domain is all real numbers.
The range is y> 0.
The equation of the asymptote is y = 0
The y-intercept is 1
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