(b) Given D = [₁2³], decode the following message: Message: -1, 4, 30, -41, 39, -58, 22, -33, 31, -46, 23, -34, 1, 1 (c) Find the matrix corresponding to the quadratic form: Q(x) = 8x² + 7x2 − 3x² − 6x₁x₂ + 4x₁x3 - 2x2x3 - What is the definiteness of Q? (d) Find the quadratic form corresponding to the matrix: /1 1 0 B = 1 4 2 10 2 3/ What is the definiteness of B?
(b) Given D = [₁2³], decode the following message: Message: -1, 4, 30, -41, 39, -58, 22, -33, 31, -46, 23, -34, 1, 1 (c) Find the matrix corresponding to the quadratic form: Q(x) = 8x² + 7x2 − 3x² − 6x₁x₂ + 4x₁x3 - 2x2x3 - What is the definiteness of Q? (d) Find the quadratic form corresponding to the matrix: /1 1 0 B = 1 4 2 10 2 3/ What is the definiteness of B?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Assist with full explanation of b, c and d.
![(a) Given
2
'11
A = 4 1
-8)
-3
-8 -1 6
Using Elementary Row Operations find the rank of A.
-31
(b) Given D = [₁23] decode the following message:
Message: -1, 4, 30, -41, 39, -58, 22, -33, 31, -46, 23, -34, 1, 1
(c) Find the matrix corresponding to the quadratic form:
Q(x) = 8x² + 7x² − 3x² - 6x₁x₂ + 4x1x3 - 2x₂x3
What is the definiteness of Q?
(d) Find the quadratic form corresponding to the matrix:
What is the definiteness of B?
1
B = 1
0
1 0
4 2
2 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb72e28a-40cf-4e0b-babe-9ae5dd59d0fc%2Fc1ae3b75-06a9-4c11-95b4-4ca7c0767f0e%2Fqpgnhnm_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Given
2
'11
A = 4 1
-8)
-3
-8 -1 6
Using Elementary Row Operations find the rank of A.
-31
(b) Given D = [₁23] decode the following message:
Message: -1, 4, 30, -41, 39, -58, 22, -33, 31, -46, 23, -34, 1, 1
(c) Find the matrix corresponding to the quadratic form:
Q(x) = 8x² + 7x² − 3x² - 6x₁x₂ + 4x1x3 - 2x₂x3
What is the definiteness of Q?
(d) Find the quadratic form corresponding to the matrix:
What is the definiteness of B?
1
B = 1
0
1 0
4 2
2 3.
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