![[47 b) [5 marks] Let X1 =12] and Let X, = 5 be two solutions of the linear [3] [6] system AX = B. Find all solutions X3 of th](http://img.homeworklib.com/questions/76544210-05d8-11eb-9d6a-ff4d8595b10b.png?x-oss-process=image/resize,w_560)
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what is all solutions of X3 of the system ( b) [5 marks] Let X= 2...
what is all solutions of X3 of the system
( b) [5 marks] Let X= 2 and Let X2 = 5 be two solutions of the linear 3 system AX = B. Find all solutions X3 of this system, such that X3 # Xand X3 # X2 l]
Question 6: [12 Marks: 5, 3, 41 Let X1, X2, ..., X6 be a random sample...
Question 6: [12 Marks: 5, 3, 41 Let X1, X2, ..., X6 be a random sample from a population following a Gamma distribution with parameters a and B. Consider the following two estimators of the mean (a/b) of this distribution. Ô2 = X And ôz = ž (X1 + X2 + X3) +ś (X4 + X5 + X3) Where I = (X1 + X2 + ... + X6) (a) Determine the sampling distribution of 7 using moment generating functions. (b)...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2) using existence and uniq...
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2) using existence and uniqueness theorem and (3) calculating et in two ways.
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2)...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaus...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Solve the given system of linear equations by Gauss-Jordan elimination: -X1 + x2 + x3 =...
Solve the given system of linear equations by Gauss-Jordan elimination: -X1 + x2 + x3 = 5 5x + 3x, – x3 = 3 2x + 4x2 + x3 = 11 [6 marks]
e) The temparature at the point y,z) is given by T(x,y,z) x2yz °C Use the method...
e) The temparature at the point y,z) is given by T(x,y,z) x2yz °C Use the method of tagrane multipliers to find the hottest and coldest points on the surface of the sphere x2y2z2 12. What are the hottest and coldest temperatures on the surface of the sphere in degrees Celsius? Question 2. (6 marks+ 4 marks+ 2 marks+3 marks+5 marks 20 marks) a) Find all solutions of the system of linear equation Ax = b where 2 3 12 5...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1...
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1 + 2x2 –x3= 18, x1 + 3x2+ x3 = 16, has the solution x=(3, 4,2)T. Using the initial guess x (0)=(1, 1,1)T Solve the above system as is using: Gauss-Seidel method. If the error increases, what does that mean and what should you do? (see b below) Condition the system so that convergence is secured and solve using the Gauss-Siedel method. Q2: Find a system...
Solve b and c only a) i. A numcrical scheme is known to perform best if...
Solve b and c only
a) i. A numcrical scheme is known to perform best if the height of the uniform subinterval is small enough in the interval (0.2]. The equation that gives the height h of the uniform subinterval is given by f(h) = 3 +h-1=0 Use the fixed point method of finding roots of equations to find the height h for which the scheme performs best. Conduct only four (4) iterations. 6 Marks ii. find algebraically all the...
Write the system of linear equations in the form Ax = b and solve this matrix...
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. x1 – 2x2 + 3x3 = 24 -X1 + 3x2 - x3 = -11 2x1 – 5x2 + 5x3 = 42 X1 x2 = X3 ] 24 -11 42 [ x
what is all solutions of X3 of the system
( b) [5 marks] Let X= 2 and Let X2 = 5 be two solutions of the linear 3 system AX = B. Find all solutions X3 of this system, such that X3 # Xand X3 # X2 l]
Question 6: [12 Marks: 5, 3, 41 Let X1, X2, ..., X6 be a random sample from a population following a Gamma distribution with parameters a and B. Consider the following two estimators of the mean (a/b) of this distribution. Ô2 = X And ôz = ž (X1 + X2 + X3) +ś (X4 + X5 + X3) Where I = (X1 + X2 + ... + X6) (a) Determine the sampling distribution of 7 using moment generating functions. (b)...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2) using existence and uniqueness theorem and (3) calculating et in two ways.
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2)...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Solve the given system of linear equations by Gauss-Jordan elimination: -X1 + x2 + x3 = 5 5x + 3x, – x3 = 3 2x + 4x2 + x3 = 11 [6 marks]
e) The temparature at the point y,z) is given by T(x,y,z) x2yz °C Use the method of tagrane multipliers to find the hottest and coldest points on the surface of the sphere x2y2z2 12. What are the hottest and coldest temperatures on the surface of the sphere in degrees Celsius? Question 2. (6 marks+ 4 marks+ 2 marks+3 marks+5 marks 20 marks) a) Find all solutions of the system of linear equation Ax = b where 2 3 12 5...
Solve b and c only
a) i. A numcrical scheme is known to perform best if the height of the uniform subinterval is small enough in the interval (0.2]. The equation that gives the height h of the uniform subinterval is given by f(h) = 3 +h-1=0 Use the fixed point method of finding roots of equations to find the height h for which the scheme performs best. Conduct only four (4) iterations. 6 Marks ii. find algebraically all the...
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. x1 – 2x2 + 3x3 = 24 -X1 + 3x2 - x3 = -11 2x1 – 5x2 + 5x3 = 42 X1 x2 = X3 ] 24 -11 42 [ x
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