Let TE B(H) be a self-adjoint operator on a Hilbert space H (a) Use the continuous functional calculus to show that T20 if o(T) C [0, ∞). (b) Show that T is an orthogonal projection if and only if (T) C {0, 1}.

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: factors of 24 that add up to 10

A: factors of 24 that add up to 10

Q: 21 2. 6.

A:

Q: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: 1/3+2/9

A: Given 1/3 + 2/9

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 10 8/10 + 9 7/12=

A:

Q: 6. 1, 5, 11, 19, 29, 7. 1, 4, 10, 20, 35, 1 1 1 1 1 8. 1, | 2 3´4´5´6 3 7 9 9. 1•2 3•4 5•6´7•8 10.…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: 7 items chosen 5 at a time

A:

Q: 6 2/5 + 1 3/10

A:

Q: (5V3)2

A: Explanation of the solution is given below...

Q: 7/2 + 3 4/6

A:

Q: 5/14+1/6

A: 514+16=15+742

Q: 22n+1 3n+1 2.

A:

Q: expand (a-b)7

A: The solution is given in the next step.

Q: 1 7. 27 2.

A:

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: 9/12+3/24

A:

Q: 16 2/5- 8 4/9

A:

Q: reduce to fraction Simptry to 0.82= Towest terms 0.60 2

A:

Q: 42. The term that does not contain x in the expansion of 8x +

A:

Q: -3n in

A:

Q: 57-24

A: Given that: 57-24

Q: W 4. What is the value of the 4th term of the expansion (a + b)"? O a5 O 5a*b O 10a²63 10a b?

A:

Q: Evaluabe: 25+3 se

A: Here we find Laplace inverse transform

Q: (1– 3csc(

A:

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

A:

Q: 5 2/5+ n= 75/6

A: Given query is to find the value of n.

Q: 1. Use expansion along the 3rd row -4 3 1 2 -1 1 7 5

A:

Q: mplify. (76)2

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.