6. Assume that the following determinant calculation is correct. i. Use the properties of determinants (3.2.4 in the Study Guide or p30 - p37 of the lecture notes) to evaluate the following determinants. Identify the relevant property(s) and show the required working but do not calculate the determinants directly (i.e. don't expand using cofactors and minors). ii. 1 002 1 2 13 4 1 00 1250 iii. 1 1 10 022 0 0 15 4 2301 = -32 12 13 0041 1002 1 250 10 24 12 0252 2603 00 12 3
Assume that the following determinant calculation is correct.
1 0 0 2
1 2 1 3
0 0 4 1
1 2 5 0
= −32
Use the properties of determinants (3.2.4 in the Study Guide or p30 - p37 of the lecture notes)
to evaluate the following determinants. Identify the relevant property(s) and show the required
working but do not calculate the determinants directly (i.e. don’t expand using cofactors and
minors).
i.
1 1 1 0
0 2 2 0
0 1 5 4
2 3 0 1
ii.
1 2 1 3
0 0 4 1
1 0 0 2
1 2 5 0
iii.
1 0 0 2
2 4 2 6
1 2 5 0
0 0 12 3
iv.
1 0 4 5
1 2 1 3
0 0 4 1
1 2 5 0
v. In addition to the properties in the Study guide, for the following you can also use the
result that the determinant of an upper triangular matrix can be found by multiplying along
the diagonal.
det
([
1 1 1 0
0 2 2 0
0 1 5 4
2 3 0 1
]
[
1 5 3 0
0 3 2 0
0 0 −1 4
0 0 0 2
])
![iii.
iv.
det
10
24
0120
0252
1
0
2
6
0
12 3
1045
1 2 1 3
0 0 4 1
1250
v. In addition to the properties in the Study guide, for the following you can also use the
result that the determinant of an upper triangular matrix can be found by multiplying along
the diagonal.
1 1 1 0] [1 5 3 0
0220 03 2 0
015 4 0 0 -1 4
230 1 0 0 0 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb40d4a8a-1252-42a3-9f75-93bf3e960f9c%2Faa7f46b1-2616-4734-bc8f-e66c2cdb22e4%2Fovrdau_processed.png&w=3840&q=75)
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