Wronskian; linear algebra

Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: x, e^x, xe^x, x in any interval

Linear Algebra : Wronskian

Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: x^2 - x, x^2 + x, x^2, all x

Linear algebra

Determine the characteristic values of the given matrix and find the corresponding vectors: [ -1 1 ] [ 4 2 ]

Vectors and Characterisitic Values of a Matrix

Determine the characteristic values of the given matrix and find the corresponding vectors: [ 1 -2 ] [ 2 -3 ]

Characteristic Values of a Matrix and Corresponding Vectors

Determine the characteristic values of the given matrix and find the corresponding vectors: [ 1 2 -1 ] [ 0 -2 0 ] [ 0 -5 2 ]

Linear algebra

Determine the characteristic values of the given matrix and find the corresponding vectors: [ 2 -2 1 ] [ 1 -1 1 ] [ -3 2 -2 ]

Matrices, Reciprocals and Characteristic Vectors

If A is nonsingular, show that the characteristic values of A^(-1) are the reciprocals of A, and that A and A^(-1) have the same characteristic vectors.

Differential Equation : Basis

Verify that the given functions form a basis for the space of solutions of the given differential equation: x^2 y'' - 2xy' + 2y = 0, f_1(x) = x, f_2(x) = x^2, x > 0

Differential Equation

For the following differential equation find all numbers r, real and complex, such that e^(rx) is a solution; find two linearly independent real solutions: (D^2 - 3D + 2) y = 0

Differential equation

Find the general solution of the differential equation: y'' + 2y' = 0