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general order n x n
2.21 Find the determinant and inverse of the nxn matrix 10...
Compute the determinant of the following n x n matrix: [ 2-1 -1 2-1 -1 2...
Compute the determinant of the following n x n matrix: [ 2-1 -1 2-1 -1 2 2 -1 -1 2 (All "missing" entries are 0.) This is a nice exercise in mathematical induction. To do this problem, first try computing a few specific cases, then make a conjecture about the general nxn determinant. Then prove that your conjecture is correct by induction. (Actually, you will use strong induction, where you assume that the determinant in the nxn case follows from...
a) suppose that the nxn matrix A has its n eigenvalues arranged in decreasing order of absolute size, so that >>....
a) suppose that the nxn matrix A has its n eigenvalues arranged
in decreasing order of absolute size, so that >>....
each eigenvalue has its corresponding eigenvector, x1,x2,...,xn.
suppose we make some initial guess y(0) for an eigenvector.
suppose, too, that y(0) can be written in terms of the actual
eigenvectors in the form y(0)=alpha1.x1 +alpha2.x2
+...+alpha(n).x(n), where alpha1, alpha2, alpha(n) are constants.
by considering the "power method" type iteration y(k+1)=Ay(k) argue
that (see attached image)
b) from an nxn...
Use the fact that cA| = |A to evaluate the determinant of the nxn matrix. A=...
Use the fact that cA| = |A to evaluate the determinant of the nxn matrix. A= - [1 12 15 3 -9 STEP 1: Factor out the greatest common divisor. 12 15 3 -9 = STEP 2: Find the determinant of the matrix found in Step 1. STEP 3: Find the determinant of the original matrix.
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is...
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5...
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5 1 0 (b) Let N be a nxn matrix with N2 = 0. Show (I. - N)-1 = IA+N. (Hint: Use the definition of the inverse.)
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2...
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
5. (10 points) Find the determinant of the given matrix A by using cofactor expansion. Then...
5. (10 points) Find the determinant of the given matrix A by using cofactor expansion. Then find the determinant of A. 1 2 A= | -2 3 3 -5 5 1 7 0 /
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforwar...
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
3. A. Find the Determinant of this VC matrix: 0 0.5 1 B. Now find the...
3. A. Find the Determinant of this VC matrix: 0 0.5 1 B. Now find the Inverse. C. Given that C-7 (you can work this out yourself), what are the weights for the global minimum variance portfolio? D. what is the variance for this portfolio?
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for...
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...
Compute the determinant of the following n x n matrix: [ 2-1 -1 2-1 -1 2 2 -1 -1 2 (All "missing" entries are 0.) This is a nice exercise in mathematical induction. To do this problem, first try computing a few specific cases, then make a conjecture about the general nxn determinant. Then prove that your conjecture is correct by induction. (Actually, you will use strong induction, where you assume that the determinant in the nxn case follows from...
a) suppose that the nxn matrix A has its n eigenvalues arranged
in decreasing order of absolute size, so that >>....
each eigenvalue has its corresponding eigenvector, x1,x2,...,xn.
suppose we make some initial guess y(0) for an eigenvector.
suppose, too, that y(0) can be written in terms of the actual
eigenvectors in the form y(0)=alpha1.x1 +alpha2.x2
+...+alpha(n).x(n), where alpha1, alpha2, alpha(n) are constants.
by considering the "power method" type iteration y(k+1)=Ay(k) argue
that (see attached image)
b) from an nxn...
Use the fact that cA| = |A to evaluate the determinant of the nxn matrix. A= - [1 12 15 3 -9 STEP 1: Factor out the greatest common divisor. 12 15 3 -9 = STEP 2: Find the determinant of the matrix found in Step 1. STEP 3: Find the determinant of the original matrix.
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5 1 0 (b) Let N be a nxn matrix with N2 = 0. Show (I. - N)-1 = IA+N. (Hint: Use the definition of the inverse.)
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
5. (10 points) Find the determinant of the given matrix A by using cofactor expansion. Then find the determinant of A. 1 2 A= | -2 3 3 -5 5 1 7 0 /
Problem X. Take the method for finding the inverse of a given n x n matrix A -a by straightforward Gauss (or Jordan) elimination (Problem 7 is a particular case for n 3). First you write down the augmented matrix A and apply the Gauss process to this as discussed in class: A-la2,1 a2,2 a2,n : an,1 an,2 .. an.n 0 0 1 3. Derive the Jordan elimination algorithm without pivoting for the augmented matrix in terms of a triple...
3. A. Find the Determinant of this VC matrix: 0 0.5 1 B. Now find the Inverse. C. Given that C-7 (you can work this out yourself), what are the weights for the global minimum variance portfolio? D. what is the variance for this portfolio?
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...
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