.1 2 1 A2
1, Consider the matrix A : O 1 0 1 .
2 —1 1 2
(a) (6 points) Determine a. basis for the colnmn Space consisting of coium'ns of A;
(b) (2 points) What is the dimension of the row space of A?
(c) {2 points) Find the rank and nulllity of A.~
,.
1 0
0 1
1 {J 0 0
0 U 1 0 “ 5
1. (15 points) Compute the determinant of the matrix
2015 2015 2015 2015
{ x + ay + z m 0
2. Find the value(s) of the real numbers a, b for which the system —x + ay — z : 2 has (a) (5
points) no solution, or (b) (5 points)
PRACTICE TEST 2
TIME LIMIT: 80 min
1. (15 points) Compute the determinant of the matrix
1
2
1
0
1
1
2
1
0 2016
0
1
1
0
0
1
1
0
0 2016
1
2
1
2
0
.
2. Let V be the set of all the vectors in R4 of the form [a b, a c, a + b c, b c]T , where a, b, c
are real
Math343 Test #2 October 26, 2012
Directions: Show all work. Answers without work generally do not earn points. This test has 60
points, but is scored out 50 {scores capped at 50).
1 [.3 parts, 3 points each] Find the éeterminant of the following matrice
Mat11343 Test #1 September 28, 201%
Name: S S
Directions: Show all work. Answers Without work generally do not; earn points. This test has 68
points.
1. [2 parts, 6 points each] Soive the following linear $ys1;ems.
(a) 5i: : i
53L "3 I in 4L 1 f
0
1
0
1
1
0
0
0
.
1. (15 points) Compute the determinant of the matrix
0
0
1
0
2015 2015 2015 2015
x + ay + z = 0
2. Find the value(s) of the real numbers a, b for which the system x + ay z = 2 has (a) (5
x
+z =b
points) no solution, or (b) (5 poin