MATH 307B FALL 2011 PRACTICE TEST #2
Write clearly. All questions carry equal weight.
(1) Consider the matrix
2 2 0
A = 1 1 1
110
(a) Give a set of vectors that span the null space of A.
(b) Is the linear transformation LA : R3 R3 ; x Ax injective (1-1)?
MATH 307B FALL 2011 PRACTICE TEST #5
Write clearly. Show your working. All questions carry equal weight.
(1) Suppose x1 = [1 0 1]T and x2 = [1 2 1]T . Find an orthogonal basis for the span of
the set cfw_x1 , x2 .
(2) Suppose y = [1 1 2]T , u1 = [1 2 0]T
MATH 307B FALL 2011 PRACTICE TEST #3
Write clearly. All questions carry equal weight.
p(0)
(1) Consider the transformation T : P3 R3 ; p(t) p (0) . Is it linear? Justify your answer.
p (0)
(2) Consider the matrix
2010
A = 1 1 1 1 .
3121
Determine each of
MATH 307B FALL 2011 PRACTICE TEST #4
Write clearly. All questions carry equal weight.
(1) Suppose that A is a 10 10 matrix, with det A = 2. Compute det(2A5 ).
(2) Compute the determinant
2 1
ab
00
2 1
3
c
0
2
0
0
.
2
0
(3) Compute the real eigenvalues of
MATH 307B FALL 2011 PRACTICE TEST #1
Write clearly. All questions carry equal weight.
(1) Following are the augmented matrices of systems of equations. In each case, determine
whether the corresponding system has a unique solution, innitely many solutions