5. Let A Є Mnxn (F) be an invertible matrix, and let u E F" be a column vector. For each 1≤i≤n let A,(u) be the matrix obtained from A by replacing the ith column of A with u. Also, let 1 xi= det A, (u)/ det A, and let x E F" be the column vector x = Show that Ax = u. In

If x ER" is a column vector (i.e. an n x1 matrix), then In-2xx' is always a symmetric matrix. True False

Suppose A is the 3 by 3 matrix ones(3, 3) of all ones. Find two independent vec- tors x and y that solve Ax = 0 and Ay 0. Write that first equation Ax = 0 (with numbers) as a combination of the columns of A. Why don't I ask for a third independent vector with Az = 0? -