Math 205 A B Quiz 06 gold page 1 11/02/2012 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
2. Let B=
1 2 4
a b c
r s t
; suppose det(B)=5
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)
2a) M=
1a r
2b s
4c t
2b) N=
1 2 4
a b c
r+ 2 s+ 4 t+ 8
2c) Q=
10 20 40
a b c
r s t
2d) R=
10 20 40
a b c
124
2e) S= 4B
3) Suppose the following elementary row operations turn the matrix Ainto U:
First, rows r1and r2are swapped. Second, r3←r3+ 10r2, Third, row 1 is multiplied by 4. The matrix Uis a 3 ×3 upper
triangular matrix, with main diagonal entries 4, 3, and 2.
3A) What is det(A)? Explain.
3B) Is Ainvertible? Explain how you know.