Linear Algebra

Determine whether the system x + y = 2 and 2x + 2y = 5 is consistent or inconsistent.

Determine whether the vectors (1, 0), (0, 1), and (1, 1) form a basis for R^2.

Determine whether the vectors v1 = (1, 2) and v2 = (3, 6) are linearly independent.

Determine whether T: R^2 → R^2 defined by T(x, y) = (x + y, 2x + 2y) is one-to-one.

Express v = (7, 1) as a linear combination of u1 = (1, 1) and u2 = (2, -1).

Find an eigenvector corresponding to the eigenvalue λ = 3 for A = [[2, 1], [1, 2]].

Find the determinant of A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]].

Find the determinant of A = [[4, 7], [2, 5]].

Find the dot product of u = (2, -1, 3) and v = (4, 5, -2).

Find the eigenvalues of A = [[2, 1], [1, 2]].