Homework Answers
in the basis i,j,k we can define out position vector as ai+bj+ck for position (a,b,c)
its reflection along xy-plane will just change its 3rd coordinate or z coordinate multiplied by -1
i.e. our required coordinates are (a,b,-c)
so our matrix would be
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3. Find the matrix for the symmetry operator with respect to the plane xOy in the...
3. Find the Kernel and the Range for the projection operator onto the plane z =...
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_}...
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_} -). with respect to the basis E = [(1,1), (1, -1)7]. (a) Find B = [L], with respect to the basis F= |(1,0), (2, 1)T] .
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with...
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with respect to the basis (4.3).(1,1) of R
the plane x -y 0 Find the Kemel and the Range for the projection operator ont n the basis the plane x -y 0 Fin...
the plane x -y 0 Find the Kemel and the Range for the projection operator ont n the basis
the plane x -y 0 Find the Kemel and the Range for the projection operator ont n the basis
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator...
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator on R whose matrix representation with respect to the ordered basis . is a) Determine the transition matrix (change of basis matrix) from, v,to (1) (Draw the commutative triangle). 3 b) Find the matrix representation B, of L with respect to ,v} by USING the similarity relation
B is the matrix of T: V → V with respect to a basis H, and...
B is the matrix of T: V → V with respect to a basis H, and S is the transition matrix from a basis G to H. Find the matrix A of Twith respect to G. B = 6 %). S= ($ 3).
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0,...
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
Consider the operator a) Express the operator in matrix form, in the IPs), IP2),4) basis. b)...
Consider the operator a) Express the operator in matrix form, in the IPs), IP2),4) basis. b) Is the operator hermitian ? c) Find the normalized eigenvectors d) Verify the completeness of the vector space e) Write down all of the projection operators f) Suppose the state of a system is described by the state vector: Find the probabilities of measuring each of the eigenvalues of the operator in this state.
only do (e)-(g) The linear operator L : R3 + R3 is given by its matrix...
only do (e)-(g) The linear operator L : R3 + R3 is given by its matrix A = Al,s wit respect to the standard basis S = {(1, 22, 23}, where To 0 11 -10- 20 [4 00 (a) Find the characteristic polynomial PL(x) of L; (b) What are the eigenvalues of L and what are their algebraic multiplicities? (e) What are the geometric multiplicities of eigenvalues of L? Is L diagonal- izable? (d) Find a basis B of eigenvectors...
If you can find a plane of symmetry in the flat hexagonal drawing of a substituted...
If you can find a plane of symmetry in the flat hexagonal drawing of a substituted cyclohexane ring, the molecule is achiral. If you cannot find a plane of symmetry, it is chiral. h. Using this simplification, determine whether the following substituted cyclo- hexane rings are chiral or achiral. Draw plane of symmetry for any achiral molecules. CH3 "Сн, CH₂ OH н, c cн, HO
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_} -). with respect to the basis E = [(1,1), (1, -1)7]. (a) Find B = [L], with respect to the basis F= |(1,0), (2, 1)T] .
36. Consider the linear operator T(x, y)- (5x-y,3x+2y) on R. Find the matrix of T with respect to the basis (4.3).(1,1) of R
the plane x -y 0 Find the Kemel and the Range for the projection operator ont n the basis
the plane x -y 0 Find the Kemel and the Range for the projection operator ont n the basis
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator on R whose matrix representation with respect to the ordered basis . is a) Determine the transition matrix (change of basis matrix) from, v,to (1) (Draw the commutative triangle). 3 b) Find the matrix representation B, of L with respect to ,v} by USING the similarity relation
B is the matrix of T: V → V with respect to a basis H, and S is the transition matrix from a basis G to H. Find the matrix A of Twith respect to G. B = 6 %). S= ($ 3).
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
Consider the operator a) Express the operator in matrix form, in the IPs), IP2),4) basis. b) Is the operator hermitian ? c) Find the normalized eigenvectors d) Verify the completeness of the vector space e) Write down all of the projection operators f) Suppose the state of a system is described by the state vector: Find the probabilities of measuring each of the eigenvalues of the operator in this state.
only do (e)-(g) The linear operator L : R3 + R3 is given by its matrix A = Al,s wit respect to the standard basis S = {(1, 22, 23}, where To 0 11 -10- 20 [4 00 (a) Find the characteristic polynomial PL(x) of L; (b) What are the eigenvalues of L and what are their algebraic multiplicities? (e) What are the geometric multiplicities of eigenvalues of L? Is L diagonal- izable? (d) Find a basis B of eigenvectors...
If you can find a plane of symmetry in the flat hexagonal drawing of a substituted cyclohexane ring, the molecule is achiral. If you cannot find a plane of symmetry, it is chiral. h. Using this simplification, determine whether the following substituted cyclo- hexane rings are chiral or achiral. Draw plane of symmetry for any achiral molecules. CH3 "Сн, CH₂ OH н, c cн, HO
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