(1 point) Find a non-zero vector x perpendicular to the vectors 1 3 -10 ✓= and ủ -3 2 2 =
2 0 If A is a square matrix then A2 = AA. Let A = Find A2 3 1 A2 = (Simplify your answer.)
(1 point) Find a non-zero vector x perpendicular to the vectors ✓ : 2 and ū -4 -2 =
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) Let a be a real constant. Consider the equation dx2 dx with boundary conditions y(0)0 and y(2) 0 For certain discrete values of a, this equation can have non-zero solutions. Find the three smallest values of a for which this is the case. Enter your answers in increasing order. a2 , аз Note: You can earn partial credit on this problem (1 point) Let a be a real constant. Consider the equation dx2 dx with boundary conditions y(0)0...
2. Write an assertion to define all the non-zero cells in the following matrix A. (10 9 8 77 10 6 5 4 0 0 3 2 Looo 1
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4 (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
(1 point) Find the characteristic polynomial of the matrix -2-20 1 -1 0 p(x)
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = ln(6 – x) + (-1/72)x^2 + (-1/648)x^3 !!! + (1/5184)x^4 + Answer: f(x) = (1/6)X (-1/38880)x' ! + ... What is the radius of convergence? Answer: R= 6
Consider a 2 x 2 matrix A that has eigenvalues 11 -2 and A2 = 5. Find the eigenvalues of A², A- and A - 21. Is the matrix A + 21 invertible? Explain. Suppose that A is a 10 x 10 matrix and that Avi V1 Av2 = 202, x = 2v1 - 02 Find real numbers a, 8 such that A’x = av. + 802