2. Let C andD be 3 x 3 matrices. Write the determinant of D in terms of the determinant of C in the following cases (e.g. det(D) = 2 det(C)). Do not compute the determinant of C. Justify your answers. (a) D= C² 1 -1 1 -k k -k (b) С %— -3 2 and D = -3 2 -1 3 -1 3 (c) D = 3C

Elementary Linear Algebra (MindTap Course List)
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Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...
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2. Let C and D be 3 x 3 matrices. Write the determinant of D in terms of the determinant of C in the
following cases (e.g. det(D) = 2 det(C)). Do not compute the determinant of C. Justify your answers.
(a) D= C²
1
-1
1
-k
k
-k
(b) C =
-3
2
and D =
-3
2
-1
3
-1
3
(c) D = 3C
2
-3
2 - k
-k
-3
(d) C =
-1
-1
and D =
-1
-1
-3
1
-3
1
4
-3
1
-3
(e) C =
1
-3
and D =
4
-3
-1
1
0 -1+ 4k 1- 3k
(f) D = CT
3. Compute the determinant of the matrix M using elementary row operations (all row operation
must be shown).
1
3
-4
1
-5
M =
2
4
-3
-3
-7
-5
2
Transcribed Image Text:2. Let C and D be 3 x 3 matrices. Write the determinant of D in terms of the determinant of C in the following cases (e.g. det(D) = 2 det(C)). Do not compute the determinant of C. Justify your answers. (a) D= C² 1 -1 1 -k k -k (b) C = -3 2 and D = -3 2 -1 3 -1 3 (c) D = 3C 2 -3 2 - k -k -3 (d) C = -1 -1 and D = -1 -1 -3 1 -3 1 4 -3 1 -3 (e) C = 1 -3 and D = 4 -3 -1 1 0 -1+ 4k 1- 3k (f) D = CT 3. Compute the determinant of the matrix M using elementary row operations (all row operation must be shown). 1 3 -4 1 -5 M = 2 4 -3 -3 -7 -5 2
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