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3. (10 marks) Suppose we devise a predictor forf as follows: n 2 e e is...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any l ER, we can write A = \I + (A – XI) (b) (10 marks) Suppose V is a proper subspace of Mn,n(R). That is to say, V is a subspace, and V + Mn,n(R) (there is some Me Mn,n(R) such that M&V). Show that there exists an invertible matrix M...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any l ER, we can write A = \I + (A – XI) (b) (10 marks) Suppose V is a proper subspace of Mn,n(R). That is to say, V is a subspace, and V + Mn,n(R) (there is some Me Mn,n(R) such that M&V). Show that there exists an invertible matrix M...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any XER, we can write A= XI + (A - XI) (b) (10 marks) Suppose V is a proper subspace of Mn.n(R). That is to say, V is a subspace, and V #Mnn(R) (there is some Me M.,n(R) such that M&V). Show that there exists an invertible matrix M e Mn.n(R) such...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothe...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
NEED HELP ESPECIALLY ON C,D,E,F 2. [6pt] We attempt to find all solutions to f(x) =...
NEED HELP ESPECIALLY ON C,D,E,F
2. [6pt] We attempt to find all solutions to f(x) = 0, where f(x) = e" – 3x – 1. (a) Sketch y = f(x) for -1 < x <3. How many solutions & does f(x) = 0 have? (b) Write code to implement the bisection method. Using the initial interval (1,3), write down the sequence of approximations X1, 22, 23, 24, 25 produced from your code. (c) What is the theoretical maximum value of...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the following bit-depth? a. 01 bit = b. 03 bit = C. 04 bit = d. 08 bit = e. 16 bit = 2. In a 4k image, the resolution is 4096 x 2160. a. How many pixels in a 4k image? b. If we divided a 4k image into a block of 8 * 8 pixels. How many blocks we will have? 3. We...
3. We want to transmit commands to a drone over a wireless channel. The commands and...
3. We want to transmit commands to a drone over a wireless channel. The commands and the probability of transmission are as follows: up (0.1), down (0.1), forward (0.4), left (0.15), right (0.15) and hover (0.1). (30) (a) What is a compact binary code to transmit these messages? (5) b) Suppose for hardware simplification reasons, a fixed 4-bit representation of each of the commands is used instead of the compact code. If a command is sent every second, how inefficient...
3. [10 marks] Suppose we would like to buy n items from SuperCheapStore (SCS); all items...
3. [10 marks] Suppose we would like to buy n items from SuperCheapStore (SCS); all items are currently priced at 1 CAD. Unfortunately there is no delivery and we have to deliver them home. The bad news are: we can fit only 1 item in our truck: it takes one day to drive home and back. There is even worse news -SCS charges us for the storage of undelivered items and the charge for storage of te i growth exponentially...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L, and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m} (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a)...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lg, Ly and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical bosons...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any l ER, we can write A = \I + (A – XI) (b) (10 marks) Suppose V is a proper subspace of Mn,n(R). That is to say, V is a subspace, and V + Mn,n(R) (there is some Me Mn,n(R) such that M&V). Show that there exists an invertible matrix M...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any l ER, we can write A = \I + (A – XI) (b) (10 marks) Suppose V is a proper subspace of Mn,n(R). That is to say, V is a subspace, and V + Mn,n(R) (there is some Me Mn,n(R) such that M&V). Show that there exists an invertible matrix M...
2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any XER, we can write A= XI + (A - XI) (b) (10 marks) Suppose V is a proper subspace of Mn.n(R). That is to say, V is a subspace, and V #Mnn(R) (there is some Me M.,n(R) such that M&V). Show that there exists an invertible matrix M e Mn.n(R) such...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
NEED HELP ESPECIALLY ON C,D,E,F
2. [6pt] We attempt to find all solutions to f(x) = 0, where f(x) = e" – 3x – 1. (a) Sketch y = f(x) for -1 < x <3. How many solutions & does f(x) = 0 have? (b) Write code to implement the bisection method. Using the initial interval (1,3), write down the sequence of approximations X1, 22, 23, 24, 25 produced from your code. (c) What is the theoretical maximum value of...
10 marks Question#3 Answer the following Questions 1. How many colors do we have at the following bit-depth? a. 01 bit = b. 03 bit = C. 04 bit = d. 08 bit = e. 16 bit = 2. In a 4k image, the resolution is 4096 x 2160. a. How many pixels in a 4k image? b. If we divided a 4k image into a block of 8 * 8 pixels. How many blocks we will have? 3. We...
3. We want to transmit commands to a drone over a wireless channel. The commands and the probability of transmission are as follows: up (0.1), down (0.1), forward (0.4), left (0.15), right (0.15) and hover (0.1). (30) (a) What is a compact binary code to transmit these messages? (5) b) Suppose for hardware simplification reasons, a fixed 4-bit representation of each of the commands is used instead of the compact code. If a command is sent every second, how inefficient...
3. [10 marks] Suppose we would like to buy n items from SuperCheapStore (SCS); all items are currently priced at 1 CAD. Unfortunately there is no delivery and we have to deliver them home. The bad news are: we can fit only 1 item in our truck: it takes one day to drive home and back. There is even worse news -SCS charges us for the storage of undelivered items and the charge for storage of te i growth exponentially...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L, and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m} (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lg, Ly and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical bosons...
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