a) The matrix B is a 3 x 3 matrix and det(B) = 3. Give the reduced row echelon form of B. b) Compute the determinant of |a a+2 a+4| b b+2 6+4 C c+2 c+4| c) Solve DX = 0 with 40000 -1 2 0 0 0 D = 260 6 10 102 5 0 7 4 -3 O 000L

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a) The matrix B is a 3 x 3 matrix and det(B) = 3. Give the reduced row echelon form of B.
b) Compute the determinant of
a
a+2 a +4
b
b+2
b+4
C
c+2
c+4
c) Solve DX = 0 with
0 0
0
0
D = 2
0 0
0
10 2 4
0 1
d) Let A and B be 2 x 2 invertible matrices. Given that det(AB-¹) = 2 and det(2AT AB) = 16, find
det(A) and det(B).
ONLA
4 0
0
2
0
1
5
07 -3
Transcribed Image Text:a) The matrix B is a 3 x 3 matrix and det(B) = 3. Give the reduced row echelon form of B. b) Compute the determinant of a a+2 a +4 b b+2 b+4 C c+2 c+4 c) Solve DX = 0 with 0 0 0 0 D = 2 0 0 0 10 2 4 0 1 d) Let A and B be 2 x 2 invertible matrices. Given that det(AB-¹) = 2 and det(2AT AB) = 16, find det(A) and det(B). ONLA 4 0 0 2 0 1 5 07 -3
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