⎡a b b b b b⎤ ⎢b a b b b b⎥
⎢⎥ 5.LetA=⎢b b a b b b⎥.
⎢b b b a b b⎥ ⎢⎥
⎢b b b b a b⎥ ⎢b b b b b a⎥
⎣⎦
(a) Express the determinant of A in terms of a and b .
(b) Find all the eigenvalues of A and the corresponding
multiplicities.
pls offer the detail of Gaussian elimination in (a )
Thank you!!
⎡a b b b b b⎤ ⎢b a b b b b⎥ ⎢⎥ 5.LetA=⎢b b a b b b⎥. ⎢b b b a b b⎥ ⎢⎥ ⎢b b b b a b⎥ ⎢b b b b b a⎥ ⎣⎦ (a) Express the determinant of A in terms of a and b . (b) Find all the eigenvalues of A and the co...
⎡a b b b b b⎤ ⎢b a b b b b⎥
⎢⎥ 5.LetA=⎢b b a b b b⎥.
⎢b b b a b b⎥ ⎢⎥
⎢b b b b a b⎥ ⎢b b b b b a⎥
⎣⎦
(a) Express the determinant of A in terms of a and b .
(b) Find all the eigenvalues of A and the corresponding
multiplicities.
could u use equations to explain what's happening here,
especially
pls offer the detail of Gaussian elimination...
1. LetA-Lind the follwing a) lA 2. Use expansion by cofactors to find the determinant of the matrix. A 4 or column that you are expanding.) 5 0(In your solution, state the row -3 6-4 3. Let u (1,-2,4,-5), (8,-10, -2,3) and w (1,0,8,0). Find the following a.) 6u 4. If possible, write vas a linear combination of ul, u2 and ug. ii! = (4,3,-2) , iz (8,6,1), u,-(-4,5,12), U = (4,-13,-17) 5. Let Wbe the set of all 3...
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
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...
U0910 jone w teyn suomar LetA= [4 3 ] and B=(2 ] - 1. Find A+B 2. Find A-B 3. Find A.B 4. Find A.A 5. Find #1 determinant of A 6. In #1 Find A 7. Find the max & min value of (=2x + 5y +8 on the given corner (0,4), (2,6),(4,1)
Also find the Eigenvalues of B
Problem 2 Compute the determinant of 1 0 0 B - XId, where Id = 10 1 0 C: 0 0 1 B= 1 0 0 2 1 -2 3 2 1
Tk 1 21 5 -5 k (a) Find the determinant of A in terms of k (b) For which value(s) of k is the matrix A invertible? (c) Let B-(k,1,2,0), (0, k, 2,0),(5,-5, k,0)) be a set of vectors in R4, and let k equal some answer you gave for part (b) of this question. Add an appropriate number of vectors to B so that the resulting set is a basis for R'
Tk 1 21 5 -5 k (a)...
Question 1: Given the following matrix A. 02 A- 1 2 3 2 (a) Find the determinant of A (b) Find eigenvalues and the corresponding eigenspaces of A (c) Determine whether A is diagonalizable. If so, find a matrix P and a diagonal matrix D such that P-1AP=D If not, justify your answer. (d) Find a basis of Im(A) and find the rank of Im(A) (e) Find a basis of Ker(A) and find the rank of Ker(A)
Question 1: Given...
Express the Slater determinant (total wave function) for the
ground-state configuration of Boron (B) in terms of orbitals such
as 1s, 2s, ··· and spins such as and .
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
4 Matrix A is defined as A = [3_21 (a) Find the eigenvalues. (5 marks) (b) Find a corresponding eigenvector for each of the eigenvalues found in (a). (10 marks) (c) Use the above (a) and (b) results to solve the vector-matrix differential equation * = 1} 21x with the initial conditions X(O) = (0) (10 marks)