linear algebra

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. Show that the set of all elements of R^2 of the form (1, a), where a is any real number, is not a subspace of R^2.

linear algebra

Show that the set of all elements of R^3 of the form (a + b, -a, 2b), where a and b are any real numbers, is a subspace of R^3. Show that the geometric interpretation of this subspace is a plane and find its equation.

linear algebra

Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. If S is any finite set of elements of a vector space V that contains the zero element of V, show that S is linearly dependent.

Determine whether the given set of 2x2 matrices are linearly independent

The set of all 2 x 2 real matrices constitutes a real vector space. Determine whether the given set of elements is linearly independent: [ 2 3 ] , [ -1 2 ] ,[ 1 0 ] [ 1 1 ] [ 0 0 ] [ 0 1 ]

Wronskian; linear algebra

. Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. Compute the Wronskian of the given set of functions, then determine whether the function is linearly dependent or linearly independent: cos ax, sin ax, a  0, x in any interval