Compute ? ? 10? ? using eigenvalues and eigenvectors of the matrix a
a=
1 14 4
-1 6 -2
-2 24 -7
v=
4
-1
-7
a) show that a has three distinct eigenvalues -1, 0, and 1.
b) determine the corresponding eigenspaces.
c) show that the eigenspaces form a basis of ? ? 3.
d) express v as a linear combination of the eigenspaces.
e) write down the corresponding augmented matrix.
f) solve the system using gauss-jordan elimination.
g) compute a10v.

Me find the value of x each figure.

The anwser cause i do not understand just plez

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?