Veryfying Solutions to Linear Equations

THE ORDERED PAIR (-2,-23/5) IS A SOLUTION TO WHICH LINEAR EQUATION? 4X+5Y= -2 Y=4/5X-3 4X= -5Y+2 OR NONE OF THESE?

In this problem, you are asked to find a new basis in which the matrix A is diagonalized.

Suppose that the matrix A is a linear operator on R(2) represented in the standard basis {i,j}, by the matrix mat(A)= [-1 3;2 4]. Find a new basis in which A is diagonalized.

This problem is a proof involving eigenvalues and eigenvectors.

If x is an eigenvector of the nxn matrix A, prove that bx is also an eigenvector.

Show that a matrix is symmetric and idempotent

Let X be a txk matrix whose columns are linearly independent. Let M=I-X(X'X)^(-1)X'. Show that M is symmetric and idempotent.

Ratio and Proportion: Cat-Mice Problem

Five cats can catch 5 mice in 5 minutes. At this rate, how many cats are needed to catch 100 mice in 100 minutes? (Hint: it is not 100.)

Equation: GCD and Mod

Find the least number N such that 1024N-11529=15625x where N and x are non-negative integers

Solving Inequalities

Solve: -4 (x+6) < -4 -4x Is the answer, x< -10; x> -10; all real numbers or no solution? Please show step by step how to solve the inequality. Also, I came up with "x<0" but I do not know if this means "no solution" or "all real numbers" Can you please explain step by step h ...continues

Factoring, 4-terms, NOT factored by grouping

4-terms - NOT factored by grouping. Factor out greatest common factor. 2-terms together. Get down to 3 terms first. 4t(xt+yt)+4t(x+y)-24x-24y

Proof: Upper and lower limits

Please see the attached file for the fully formatted problems. Let be a sequence of real numbers. We define and I’m having trouble with the following three proofs: 1) Show that 2) Show that if the limit of only exists when , then . 3) Show that if , then the limit exists, and .

Linear Algebra : Vectors - Inner Products

Given a vector w, the inner product of R^n is defined by: =Summation from i=1 to n (xi,yi,wi) [a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T Show that x and y are orthogonal with respect to this inner product. Compute the values of ...continues