Practice Midterm 1 (Solutions).pdf - Name: Math 54 Practice...

Name:
Math 54 Practice Midterm 1
GSI: Alex Zorn
1. Answer true or false, and explain your reasoning. Assume that A is a 4 × 3 matrix with 3
pivots. Let T denote the linear transformation defined by T ( x ) = A x .
(a) The matrix equation A x = b is inconsistent for some b ∈ R 4 .
(b) The columns of A are linearly independent. (c) The columns of A span R
4
.
(d) The domain of T is R 4 .
(e) T is one-to-one.
(f) The matrix equation A x = b is inconsistent for every b ∈ R 4 .