Homework Answers
A matrix A is said to be similar to B if there exists an
invertible matrix such that 
a)
Given that A is similiar to scalar matrix.
Therefore, we have
b)
Let the eigenvalue of A be 
A is said to be diagonalizable if there exists an invertible matrix U such that
We know that the diagonal matrix contains the eigen values of the matrix A
But it is given that A has only one diagonal value.
Hence, by part (a), 
Therefore, by applying part (a) again, we have
c)
The given matrix has only one eigen value i.e. 1 is the only eigen value of the given matrix.
But the given matrix is not a scalar matrix. Hence, by part (b), the given matrix is not diagonalozable.
Add Answer to:
A scalar matrix is simply a matrix of the form XI, where I is the nxn...
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...
True False a) For nxn A, A and AT can have different eigenvalues. b) The vector v 0 cannot be an eigenvector of A. c) If λ's an eigenvalue of A, then λ2 is an eigenvalue of A2. True False d) If A...
True False a) For nxn A, A and AT can have different eigenvalues. b) The vector v 0 cannot be an eigenvector of A. c) If λ's an eigenvalue of A, then λ2 is an eigenvalue of A2. True False d) If A is invertible, then A is diagonalizable. e) If nxn A is singular, then Null(A) is an eigenspace of A. f) For nxn A, the product of the eigenvalues is the trace of A. True False g) If...
An n x n matrix is called nilpotent if Ak = 0 (the zero matrix) for...
An n x n matrix is called nilpotent if Ak = 0 (the zero matrix) for some positive integer k. (a) Suppose A is a nilpotent nxn matrix. Prove that is an eigenvalue of A. (b) Must O be the only eigenvalue of A? Either prove or give a counterexample,
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
#8C17 points). Assume that A is an nxn invertible mntrix. Supply the following proo- Show your...
#8C17 points). Assume that A is an nxn invertible mntrix. Supply the following proo- Show your work. (a) If A O, prove that (1-A)-1+A+A fP then aven Ao 7- preve A++1- C1-A) (b) Prove that det(A)- A det(A) |A||for any natural norm (c) If A is an eigenvalue of A, prove that 12l (d) If ATA = I, prove that (Av)T(Av) 2 0, for any vector v. Recall
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O...
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. A is not diagonalizable because it only has two linearly independent eigenvectors
27. Prove that the determinant of the matrix 2 Y3 -I is 2, where (y)(y2()(ys)2. Prove also that the inverse of the matrix G is G(G-I)T İs an orthogonal matrix. Show also that the vector Show that the...
27. Prove that the determinant of the matrix 2 Y3 -I is 2, where (y)(y2()(ys)2. Prove also that the inverse of the matrix G is G(G-I)T İs an orthogonal matrix. Show also that the vector Show that the matrix A is an eigenvector for the matrix A and determine the corresponding eigenvalue
27. Prove that the determinant of the matrix 2 Y3 -I is 2, where (y)(y2()(ys)2. Prove also that the inverse of the matrix G is G(G-I)T İs an...
linear algebra Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0...
linear algebra
Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.
Problem 4: Suppose A = (ai)nxn is a symmetric matrix (i.e. the transpose of A agrees...
Problem 4: Suppose A = (ai)nxn is a symmetric matrix (i.e. the transpose of A agrees with itself) and a11 +0. After we use a11 to eliminate a21, ... , Anl, we obtain a matrix of the following form: (n-1)-matrix. Here c is an (n-1)-dimensional column vector and ct is its transpose, while B is an (n-1) Prove that B is also symmetric.
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r...
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r(u, v) be a parametric form for the surface S. Use the vector identity to show that Our ar-λ▽u where λ is a scalar field. [Note: no marks will be awarded for simply stating that a term is zero. If it is...
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...
True False a) For nxn A, A and AT can have different eigenvalues. b) The vector v 0 cannot be an eigenvector of A. c) If λ's an eigenvalue of A, then λ2 is an eigenvalue of A2. True False d) If A is invertible, then A is diagonalizable. e) If nxn A is singular, then Null(A) is an eigenspace of A. f) For nxn A, the product of the eigenvalues is the trace of A. True False g) If...
An n x n matrix is called nilpotent if Ak = 0 (the zero matrix) for some positive integer k. (a) Suppose A is a nilpotent nxn matrix. Prove that is an eigenvalue of A. (b) Must O be the only eigenvalue of A? Either prove or give a counterexample,
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
#8C17 points). Assume that A is an nxn invertible mntrix. Supply the following proo- Show your work. (a) If A O, prove that (1-A)-1+A+A fP then aven Ao 7- preve A++1- C1-A) (b) Prove that det(A)- A det(A) |A||for any natural norm (c) If A is an eigenvalue of A, prove that 12l (d) If ATA = I, prove that (Av)T(Av) 2 0, for any vector v. Recall
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. A is not diagonalizable because it only has two linearly independent eigenvectors
27. Prove that the determinant of the matrix 2 Y3 -I is 2, where (y)(y2()(ys)2. Prove also that the inverse of the matrix G is G(G-I)T İs an orthogonal matrix. Show also that the vector Show that the matrix A is an eigenvector for the matrix A and determine the corresponding eigenvalue
27. Prove that the determinant of the matrix 2 Y3 -I is 2, where (y)(y2()(ys)2. Prove also that the inverse of the matrix G is G(G-I)T İs an...
linear algebra
Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.
Problem 4: Suppose A = (ai)nxn is a symmetric matrix (i.e. the transpose of A agrees with itself) and a11 +0. After we use a11 to eliminate a21, ... , Anl, we obtain a matrix of the following form: (n-1)-matrix. Here c is an (n-1)-dimensional column vector and ct is its transpose, while B is an (n-1) Prove that B is also symmetric.
Suppose that a scalar field is constant on a surface As shown in the lectures. there are two methods that one might use to obtain the normal to the surface, and they give the same direction (a) Let r(u, v) be a parametric form for the surface S. Use the vector identity to show that Our ar-λ▽u where λ is a scalar field. [Note: no marks will be awarded for simply stating that a term is zero. If it is...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago