Consider a linear system whose augmented matrix is of the form
(1) For what values of a and b will the system have infinitely many solutions?
(2) For what values of a and b will the system be inconsistent?
True or false, with reason if true or counterexample if false:
(1) If A is invertible and its rows are in reverse order in B , then B is invertible.
(2) If A and B are symmetric then AB is symmetric.
(3) If A and B are invertible then BA is invertible.
(4) Every nonsingular matrix can be factored into the product A = LU of a lower
triangular L and an upper triangular U .
Let u1 = (1,1,1)T , u2 = (1,2,2)T , u3 = (2,3,4)T .
(1) Find the transition matrix corresponding to the change of basis from [e1, e2 , e3 ]
to [u1, u2 , u3 ] .
(2) Find the coordinates of the vector (3,2,5)T with respect to [u1, u2 , u3 ] .
Compute the Gram-Schmidt QR factorization of the matrix
Sketch the following conic section, giving axes of symmetry and asymptotes (if any).
16x12 + 24x1x2 + 9x22 − 3x1 + 4x2 = 5
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