PLEASE answer all the parts please show all your work please.This question was already answered incorrectly. 2. Let C and D be 3 x 3 matrices. Write the determinant of D in terms of the determinant of C in thefollowing cases (e.g. det(D) = 2 det(C)). Do not compute the determinant of C. Justify your answers.(a) D= C²1-11-k-k(b) С%D-32and D =-32-13-13(c) D = 3C-32 - k-k-3(d) С %—-1-1and D =-1-10.2-312-314-31-3(е) С %—12-3and D =4-3-11-1+4k 1- 3k(f) D= CT2.

Answered: Let C and D be 3 x 3 matrices. Write…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

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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PLEASE answer all the parts please show all your work please. This question was already answered incorrectly.

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
(b) С%D
-3
2
and D =
-3
2
-1
3
-1
3
(c) D = 3C
-3
2 - k
-k
-3
(d) С %—
-1
-1
and D =
-1
-1
0.
2
-3
1
2
-3
1
4
-3
1
-3
(е) С %—
1
2
-3
and D =
4
-3
-1
1
-1+4k 1- 3k
(f) D= CT
2.

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You have posted multiple sub-parts. As per the instruction, we will be solving only 3 sub-parts. We will be solving first three sub-parts as nothing is specified. If you need an answer to others then kindly re-post the question by specifying it.

We are given that $C_{3 \times 3}$ and $D_{3 \times 3} .$

For (a),

Given: $D = C^{2} .$

Now,

$\begin{array}{rcl} d e t (D) & = & d e t (C^{2}) \\ = & d e t (C \cdot C) \\ = & d e t (C) \cdot d e t (C) (we know that d e t (A B) = d e t (A) d e t (B)) \\ \Rightarrow & d e t (D) = {(d e t (C))}^{2} . \end{array}$

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