Matrices

4. (a) By first using algebraic manipulation of the matrix equation 7X - 6A = 4X - 3B, and then substitution... (See attached file)

Integral Equation

Verify that the solution of u"=f(x), u(0)=0, u(1)=0 given by u(x)= the integration from 0 to 1 of k(x,y)f(y)dy. Use Leibniz rule. (See attachment for full question)

Finding Eigenvalues / Eigenfunctions for Integral Operators

Please see the attached file for the fully formatted problems. Find the eigenvalues and eigenfunctions for the integral operator , where . (Answer: ) How would we solve the same problem if ? (Answer: )

Find the gradient using vector notation and the y intercept.

y = 2x+5

Integral Equation

see attachment Show that the following integral equation is equivalent to a differential equation. Find the resolvent (or pseudo-resolvent) operator, and solve the integral equation.

Finding Adjoint Operators

Problem: Find the adjoint operator and its domain for:... please see attached file.

Linear Algebra: Projection Matrix

See page four, the question is question # 2. Show that P^2= P^T = P and that C(P) = C(A)

Scatterplots

Tree growth scatterplot. Age 5, 14, 29, 16, 16, 26, 6, 25, 7, 18 Diameter 8, 23, 34, 24, 24, 10, 30, 14, 13 Summary points for first middle and last group based on median-median.(show cords) Equation of the line passing through the summary points. Calculate distance from line through the outer summary points to the middle p ...continues

Matrices : Row Operations and Echelon Form

1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system. Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave ...continues

Matrices : Solve by Row Reduction

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks! 1) Find the general solutions of the systems whose augmented matricies are given in a) and b). What is a general solution? a)1 -2 -1 3 3 -6 -2 2 b) 1 2 -5 - ...continues