Answer:
a.![\frac{1}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B17%7D)
b.![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)
Step-by-step explanation:
We are given that two cards are drawn are randomly selected from a standard 52- cards deck.
Total cards=52
Total number of spade cards=13
Probability=![\frac{number\;of\;favourable\;cases}{total\;number\;of cases}](https://tex.z-dn.net/?f=%5Cfrac%7Bnumber%5C%3Bof%5C%3Bfavourable%5C%3Bcases%7D%7Btotal%5C%3Bnumber%5C%3Bof%20cases%7D)
a.The probability of drawing two cards first card is spade and second card is spade without replacement =![\frac{13}{52}\times \frac{12}{51}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B52%7D%5Ctimes%20%5Cfrac%7B12%7D%7B51%7D)
The probability of drawing two cards first card is spade and second card is spade=![\frac{1}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B17%7D)
b. The probability of drawing two cards first is spade and second card is a spade with replacement =![\frac{13}{52}\times\frac{13}{52}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B52%7D%5Ctimes%5Cfrac%7B13%7D%7B52%7D)
The probability of drawing two cards first is spade and second card is a spade with replacement =![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)
Answer:
Your final answer will be, x^2 +4x -12
Step-by-step explanation:
YOUR ANSWER IS IN THE ATTACHMENT PLZZ REFER TO THE ATTACHMENT
They dont represent proportional relationship!
but what are the drop down answers?
Answer:
a) The main idea to solve this exercise is to use the identity
, where
and
are two square matrices.
Then,
. Now, recall that [\det(Id) = \det(P)\det(P^{-1})[/tex], where
stands for the identity matrix. But
, thus
and
are reciprocal to each other.
Hence,
![\det(A) =det(P)\det(D)\det(P^{-1}) = det(P)\det(P^{-1})\det(D) = \det(D).](https://tex.z-dn.net/?f=%20%5Cdet%28A%29%20%3Ddet%28P%29%5Cdet%28D%29%5Cdet%28P%5E%7B-1%7D%29%20%3D%20det%28P%29%5Cdet%28P%5E%7B-1%7D%29%5Cdet%28D%29%20%3D%20%5Cdet%28D%29.)
b) Let us write
and
. Then
![AB = (PD_AP^{-1})(PD_BP^{-1}) = PD_AD_BP^{-1}](https://tex.z-dn.net/?f=AB%20%3D%20%28PD_AP%5E%7B-1%7D%29%28PD_BP%5E%7B-1%7D%29%20%3D%20PD_AD_BP%5E%7B-1%7D)
![BA = (PD_BP^{-1})(PD_AP^{-1}) = PD_BD_AP^{-1}](https://tex.z-dn.net/?f=BA%20%3D%20%28PD_BP%5E%7B-1%7D%29%28PD_AP%5E%7B-1%7D%29%20%3D%20PD_BD_AP%5E%7B-1%7D)
But the product of two diagonal matrices is commutative, so
, from where the statement readily follows.
Step-by-step explanation: