4. For each of the following matrices A Є Mnxn (F), (i) Determine all the eigenvalues of A. (ii) For each eigenvalue A of A, find the set of eigenvectors correspond- ing to A. (iii) If possible, find a basis for F" consisting of eigenvectors of A. (iv) If successful in finding such a basis, determine an invertible matrix Q and a diagonal matrix D such that Q¹AQ = D. 3 Chap. 5 Diagonalization (a) A = (³½³ ³) for F = R 3 2 0 -2 3 (b) A = -1 1 -1 for F = R 2 2 5 (c) A = (2 ½) for F = C (d) A = 2 0 1 for F = R 20 -1

Q: Gualnete : 8! 17! (8-3)!3! (17-3)1 37!-3!5 ()!

A: We are entitle to solve only 1 question at a time. So, I am providing you the solution of first…

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A: There are 19 Girls and 19 boys.  To make them sit around a circular table the sequence can be,   G G…

Q: If n(A ∪ B) = 10, n(A) = 2 and n(B) = 12, then find n(A ∩ B).

A:

Q: (c) Doe s GCD(8 20 14). CM(8 20 14) =8. 20. 142

A: Solution

Q: n how many different ways can you seat these 19 people if no two women sit together? O C(11, 2) -…

A: woman=11man=8here 12 seating positions can be given to men and 11 position to womenso, number of…

Q: Suppose P(A) P= 0.3, P(B) = 0.4 and P(A ∩ B) = 0.12. Which of the following is Correct? A) P(A U B)…

A: The probabilities of the events are given as follows:

Q: How many five-letter passwords can be formed from the letters {A, B, J, K, X, Z} under the following…

A: From the provided information, The letters are {A, B, J, K, X, Z} Total letters = 6

Q: (1) How many paths from • to • that pass through are possible, given that you can only go right one…

A: The only one way is the answer.

Q: If  n(A) = 11, n(A ∪ B) = 13, and n(B) = 5,  then what is  n(A ∩ B)?

A:

Q: 7) In how many ways the letters of the word "BANKER" can be arranged that vowels are always…

A: The letters of the word BANKER can be arranged.

Q: In part 2) why is it K+1and K + 2 and so on(addition) instead of K1,K2,K3... (multiplication).

A: As you asked that why we use  instead of

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A: Alix and Billie found a variety of rocks and seashells on the beach. We'll explore how many…

Q: When we are considering n objects taken r at a time, with r . 1, why will the number of combinations…

A: "When we are considering n objects taken r at a time, with r . 1, why will the number of…

Q: [5 -2 31 4 B = 2 -3 2] 1 Q1/ If A = 2 1 Find: -1 Lo] а) 42 b) |A| x B in N

A:

Q: St DH+ (4) (+) (37₁) = 0 1+ck) (st S+2 S+3 S (5+3) CS+5) +K (5+2) SCS+3) CS+5) = 0 3) S (5+3) CS+5)…

A:

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: If n(A) = 6, n(A ∪ B) = 8, and n(B) = 5,  then what is  n(A ∩ B)?

A: Let A and B be any two events , the union of two events is defined as,

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A: Combination: It is nothing but the selection of objects where the order of selection is not…

Q: (4) Suppose 6 identical apples are to be shared among 3 (non- identical) children - it is not…

A: ,Here question is that 6 identical apples are to be shared among 3 non identical children.(a) so as…