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Linear Algebra

Equivalent statements

Determine which, if any, of the three statements are equivalent. a) If today is Monday, then tomorrow is not Wednesday b) It is false that today is Monday and tomorrow is not Wednesday c) Today is not Monday or tomorrow is Wednesday

Linear algebra

See attached Show that for a real symmetric matrix A=A^T, its singular values are exactly the absolute values of its eigenvalues.... Find the singular decomposition of... Verify the special theorem for the Hermitian matrix

Round-off error and Matlab

Using MatLab, compute H^-1H for various n between 5 and 15. Describe the results and comment on the difference between the MatLab output and what is expected the answer to be (given that H is invertible for all n). At what point does Matlab give a warning indicating that it may not be giving the correct answer? Try using the

Soving simultaneous equations

Solve the following pair of simultaneous equations algebraically. Any non-integer answers should be given as fractions in their simplest form. 6a + 3b = 12 8a + 2b = 6

Lp spaces and convergence

Please see the attached. you can help with either part a or b. If you can help with one of them then I will try to figure out the other. Also there is a typo on part a: Convergence of the sequence of random variables should not be in probability it is convergence almost surely. So on the top of the arrow of the given converge

Gauss-Jordan elimination word problem

A particular diet calls for exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. An individual is fed a mixture of three foods. Each gram of food 1 contains 2 units of vitamin A, 3 units of vitamin C, and 5 units of vitamin E. Each gram of food 2 contains 4 units of vitamin A, 7


Please see the attached document Thank-you for your help. For each of the following matrices, determine whether or not the matrix is diagonalizable. You may use technology to find the eigenvalues and to row reduce matrices, but that's all. Show your work and explain why the matrix is or isn't diagonalizable. (a) A=

Matrix analysis homework problem

Please see the attached Word document. Thank-you very much for your help. Suppose that A and B are n x n matrices such that A = SBS-1 (where S is an invertible matrix), so A and B are similar matrices. (a) Show: if v is an eigenvector of B with eigenvalue μ, then Sv is an eigenvector for A. (Remember that only non

Matrix theory homework05-06

Please see the attached Word document. Thank-you for your help. Suppose A and B are similar matrices, and that μ is an eigenvalue of A. We know that μ is also an eigenvalue of B, with the same algebraic multiplicity. Suppose that g is the geometric multiplicity of μ, as an eigenvalue of B. Show that μ

Matrix analysis homework

Please see the attached Word document. Thank-you for your help. 3. Suppose that A is a square matrix, and that the only eigenvectors of A are scalar multiples of the vector: Deduce as much information as you can about A, by answering the following questions. Give reasons for your answers. (a) What size is A? (b) H

Equations and inequalities

Solve the system by the substitution method 6x+5y=10 -4x+y=28 Solve the system by the elimination method 5x+5y=-11 7x-3y= 19 Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. 3x-9y=63 2x-6y= -8

Matrix Theory homework

Please see the attached file. Thank-you for your help. Let B = . Find each of the following. You may use a calculator to replace hand calculation for row reduction and finding the characteristic polynomial. Show your work; don't just write down the answers. (a) Find the characteristic polynomial of "A". (b) Find the

Solving linear equations

I don't understand how to figure out the zero factor. Problem 1: 2h - h -3=0 Problem 2: 2w (4w+1) = 1 Problem 3: x -36 = 0 Problem 4: x = 4x Problem 5: (x-3) + (x+2) = 17

Matrix theory and analysis homework

Please see the attached document and thank-you so much for your help. The matrix A = Is a 4 x 4 matrix which has eigenvalues: -3 and +2. Find the corresponding eigenspaces. For each, find a basis for the eigenspace.


See attached for full description. 4. Decide whether the pair of lines is parallel, perpendicular, or neither. 4x+5y=5 5x+4y=7 8. Solve for x. 8x-(5x+7)=14 10. Simplify. -3[87-(-55-35)] 14. Find the domain of the function. p(x) = x^2 -2x + 7 23. Solve using the substitution method. 6x+7


How do I calculate the following: 1. b/2-15=16 2. 3h+13=7

Linear algebra: eigenvector and eigenvalue

Please see attached file for full description. Show that v is an eigenvector of A and find the corresponding eigenvalue. Show that lamda is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue. 8. A = [ 2 2, 2 -1], lamda = -2 10. A = [0 4, -1 5]; lamda = 4 Use the method of Example 4.5 to find

System of linear equations and algebra word problems

Need assistance on problemsProblems needing assistance 1. What is the solution of the system? Type an ordered pair 5x+3y= -11 7x-2y= 17 2. Hockey team receives 2 points when they win and 1 point when they tie. One season, a team won a championship with 60 points. They won 12 more games than they tied. How many wins and h

Matrix Theory homework

Please see the attached document. Thanks again. This is a subset of R3. What is it, geometrically? (Give a brief description) Show that S is a subspace of R3. Find a matrix A such that...

Linear Algebra/Matrix Theory

Prove the triangle inequality starting with: |V+W|^2 You must use Re < W | V >(less than or equal to) |< V|W >| and the Schwarz inequality. Show that the final inequality becomes an equality only if |V> = b|W> where b is a real positive scalar.