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[3 marks] Consider the following statements (1) If AT A is a symmetric matrix, then A...
[3 marks] Consider the following statements (1) If AT A is a symmetric matrix, then A must be a square matrix. (ii) If A is nx n then A'(A ) - 1. (iii) If A is an nxn matrix, then tr(CA) - ctr(A). Determine which of the above statements are True (1) or False (2) So, for example, if you think that the answers, in the above order, are True False False, then you would enter "1.2.2' into the answer...
Determine if the statements are true or false. 1. If A and B are nxn matrices...
Determine if the statements are true or false. 1. If A and B are nxn matrices and if A is invertible, then ABA-1 = B. ? A 2. If A and B are real symmetric matrices of size nxn, then (AB)? = BA 3. If A is row equivalent to B, then the systems Ax = 0 and Bx = 0 have the same solution. ? A 4. If, for some matrix A and some vectors x and b we...
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.
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u...
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
(10 points)The trace of a square nxn matrix is A, denoted tr(A), is the sum of...
(10 points)The trace of a square nxn matrix is A, denoted tr(A), is the sum of its diagonal entries; that is, tr(A) = a11+2)2 +433 +: ... + ann (a) Show that tr(AB) = tr(BA) (b) Show that If A similar to B, then tr(A) = tr(B). (10 points) Let A and B are non-zero n x n matrices. (a) Show that N(A) = N(A2). Hint: Let 2 EN(A), show that is also in N(A2) and vice versa. (b) Show...
Which of the following are true for ALL nx n matrices A? Select all that apply....
Which of the following are true for ALL nx n matrices A? Select all that apply. If v is an eigenvector of A and A is invertible, then v is an eigenvector of O A™. If v is an eigenvector of A, then v is an eigenvector of A?, -3A, and A-L. If I is an eigenvalue of A, then , is an eigenvalue of AT If v is an eigenvector of A, then v is an eigenvector of A?....
Which of the following is an INCORRECT statement: 1) MATLAB command eye(n) makes an nxn identity...
Which of the following is an INCORRECT statement: 1) MATLAB command eye(n) makes an nxn identity matrix 2) Identity matrix is square matrix with ones on main diagonal and zeros elsewhere 0 3) Matrix multiplication on any array with the identity matrix changes the array 4) Matrix B is the inverse of matrix A if matrix product of A and B is the identity matrix
the last pic is number 14 please answer it as a,b,c,d as well. thanks 1. If...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
Problem 8: (11 total points) Suppose that B is a nx n matrix of the form...
Problem 8: (11 total points) Suppose that B is a nx n matrix of the form B = Viv] + v2v + V3v3, where V1, V2, V3 € R”, n > 3 are nonzero column vector and are orthogonal. a) Show that B is a positive semidefinite matrix. b) Under which condition, B will be a positive definite matrix? c) Let A be 3x3 real symmetric matrix with eigenvalues 11 > 12 > 13. Let F be a positive definite...
If A is a symmetric nxn matrix with n distinct characteristic numbers 2, show that any...
If A is a symmetric nxn matrix with n distinct characteristic numbers 2, show that any polynomial P(A) can be expressed in the form P(A) = CAP-+ +cAn-2 +...+C1_A+CH where the c’s are determined by the n simultaneous linear equations P(2) = 2** (i = 1, 2,...,n) 1)=20:45
[3 marks] Consider the following statements (1) If AT A is a symmetric matrix, then A must be a square matrix. (ii) If A is nx n then A'(A ) - 1. (iii) If A is an nxn matrix, then tr(CA) - ctr(A). Determine which of the above statements are True (1) or False (2) So, for example, if you think that the answers, in the above order, are True False False, then you would enter "1.2.2' into the answer...
Determine if the statements are true or false. 1. If A and B are nxn matrices and if A is invertible, then ABA-1 = B. ? A 2. If A and B are real symmetric matrices of size nxn, then (AB)? = BA 3. If A is row equivalent to B, then the systems Ax = 0 and Bx = 0 have the same solution. ? A 4. If, for some matrix A and some vectors x and b we...
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.
Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2...
(10 points)The trace of a square nxn matrix is A, denoted tr(A), is the sum of its diagonal entries; that is, tr(A) = a11+2)2 +433 +: ... + ann (a) Show that tr(AB) = tr(BA) (b) Show that If A similar to B, then tr(A) = tr(B). (10 points) Let A and B are non-zero n x n matrices. (a) Show that N(A) = N(A2). Hint: Let 2 EN(A), show that is also in N(A2) and vice versa. (b) Show...
Which of the following are true for ALL nx n matrices A? Select all that apply. If v is an eigenvector of A and A is invertible, then v is an eigenvector of O A™. If v is an eigenvector of A, then v is an eigenvector of A?, -3A, and A-L. If I is an eigenvalue of A, then , is an eigenvalue of AT If v is an eigenvector of A, then v is an eigenvector of A?....
Which of the following is an INCORRECT statement: 1) MATLAB command eye(n) makes an nxn identity matrix 2) Identity matrix is square matrix with ones on main diagonal and zeros elsewhere 0 3) Matrix multiplication on any array with the identity matrix changes the array 4) Matrix B is the inverse of matrix A if matrix product of A and B is the identity matrix
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
Problem 8: (11 total points) Suppose that B is a nx n matrix of the form B = Viv] + v2v + V3v3, where V1, V2, V3 € R”, n > 3 are nonzero column vector and are orthogonal. a) Show that B is a positive semidefinite matrix. b) Under which condition, B will be a positive definite matrix? c) Let A be 3x3 real symmetric matrix with eigenvalues 11 > 12 > 13. Let F be a positive definite...
If A is a symmetric nxn matrix with n distinct characteristic numbers 2, show that any polynomial P(A) can be expressed in the form P(A) = CAP-+ +cAn-2 +...+C1_A+CH where the c’s are determined by the n simultaneous linear equations P(2) = 2** (i = 1, 2,...,n) 1)=20:45
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