Math 2J Practice Midterm
The following is a practice test that is meant to give you a sense of what some possible midterm questions
might look like. This test is meant only to measure how prepared you are and what you still need to
study; it is NOT a good indicator of how well you will do on the actual midterm.
True or False
1. (
AB
)

1
=
A

1
B

1
2. If I add three times the ﬁrst row of a matrix to the second row of that matrix, I have changed the
determinant by 3.
3. If
A
is a singular matrix, then
Ax
= 0 has inﬁnitely many solutions.
4. If
AB
=
AC
and
A
6
=
O
(the zero matrix), then
B
=
C
.
5.
λ
= 0 is always an eigenvalue of a singular matrix.
6. If
A
is an
n
×
n
matrix, then det(
A
k
) = det(
A
)
k
.
7. If
A
is an
n
×
n
matrix, and
α
is a real number, then det(
αA
) =
α
det(
A
).
8. Nonsingular matrices are always row equivalent to an identity matrix.
9. Similar matrices have the same eigenvalues.
10. Overdetermined systems will always have no solution.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 DONALDSON,NEIL
 Linear Algebra, Matrices, Row echelon form

Click to edit the document details