Math Matrix Worksheet - Math 205 A B Quiz 06, 2012
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1Quiz 06 gold page 1
11/02/2012
Math 205 A B
Name
1. Find the determinant of the following matrix by hand, showing all your steps (intermediate results) along the way.
Make good use of 0’s. Circle your final answer.
2 4 0
5
5 0 0 11
12 8 3
7
9 0 0
6
1 2 4
2. Let B =
a
b
c
; suppose det(B)=5
r
s
t
Find the determinant of each of the following matrices, and under each matrix write the reason/rule/fact about determinants
of matrices you used to find the det. (eg, “swapping rows changes the sign of the det” or “the determinant of the derivative
of a matrix is the matrix of its integral” (this second fact is nonsense)
1 a r
1
2
4
2a)
M =
2
b s
2b)
N =
a
b
c
4
r + 2 s + 4 t + 8
c
t
10 20 40
10 20 40
2c)
Q =
2d)
R =
a
b
c
a
b
c
1
2
4
r
s
t
2e)
S = 4B
3) Suppose the following elementary row operations turn the matrix A into U :
First, rows r
and r
are swapped. Second, r
← r
+ 10r
, Third, row 1 is multiplied by 4. The matrix U is a 3 × 3 upper
1
2
3
3
2
triangular matrix, with main diagonal entries 4, 3, and 2.
3A) What is det(A)? Explain.
3B) Is A invertible? Explain how you know.
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