Let ● A = . 3 5 2 . 00 0 12 0 6 0 -1 L-6 3 1 0 a. Find the determinant of A using cofactor expansion b. Give a 4 x 4 triangular matrix B with determinant equal to -15 c. By carefully inspecting C, briefly justify why the determinant of C is 0 d. What would be the determinant of A²B-¹? |-- C = e. If you apply the following E.R.O.s to A : R₁ → R₂ 3R₂ → R₂ R32R4 R3 You will get a new matrix. Let's call it D. Without calculating D, what's det(D)? 1 1 150] [170 0 0 1 50 -3 1300 1 0 167 1301 3 200
Let ● A = . 3 5 2 . 00 0 12 0 6 0 -1 L-6 3 1 0 a. Find the determinant of A using cofactor expansion b. Give a 4 x 4 triangular matrix B with determinant equal to -15 c. By carefully inspecting C, briefly justify why the determinant of C is 0 d. What would be the determinant of A²B-¹? |-- C = e. If you apply the following E.R.O.s to A : R₁ → R₂ 3R₂ → R₂ R32R4 R3 You will get a new matrix. Let's call it D. Without calculating D, what's det(D)? 1 1 150] [170 0 0 1 50 -3 1300 1 0 167 1301 3 200
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 3.
Let
A =
ts
●
3
0
0
0
5
1 2
0
2
6 0
-1
-6 3 1 0
C =
e.
If you apply the following E.R.O.s to A:
R₁ R₂
• 3R₂ → R₂
.
[170
1
0
0
-3
1300
1
0
167 1301 3 200
1 150
1
50
a. Find the determinant of A using cofactor expansion
b.
Give a 4 x 4 triangular matrix B with determinant equal to -15
c. By carefully inspecting C, briefly justify why the determinant of C is 0
d. What would be the determinant of A²B-¹?
R3 -2R4 → R3
You will get a new matrix. Let's call it D. Without calculating D, what's det(D)?
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