Linear Algebra

Find the inverse of A = [[2, 1], [5, 3]].

Find the magnitude of the vector v = (3, -4, 12).

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

Given A = [[1, 2], [3, 4]] and B = [[2, 0], [-1, 5]], find AB.

Given A = [[2, 1], [-3, 4]] and B = [[5, -2], [1, 3]], find A + B.

Given u = (3, -2) and v = (5, 4), find u + v.

Given v = (2, -3, 4), find 3v.

Let T: R^2 → R^2 be defined by T(x, y) = (2x - y, x + 3y). Find the standard matrix of T.

Solve the system using row reduction: x + 2y = 7 and 3x - y = 7.

Solve the system x + y = 5 and 2x - y = 4.