Consider the matrix X and the vectors y and z below: x-E ] -- --| X= y= a. What is the inner product of the vectors y and z? (this is also sometimes called the dot product, and is sometimes written y"z) b. What is the product Xy? c. Is X invertible? If so, give the inverse, and if no, explain why not. d. What is the rank of X? Explain your answer. What does it mean that matrix A is orthonormal? What does it mean that matrix A is positive semi-definite? A is a matrix. What is the definition of its pseudoinverse?
Consider the matrix X and the vectors y and z below: x-E ] -- --| X= y= a. What is the inner product of the vectors y and z? (this is also sometimes called the dot product, and is sometimes written y"z) b. What is the product Xy? c. Is X invertible? If so, give the inverse, and if no, explain why not. d. What is the rank of X? Explain your answer. What does it mean that matrix A is orthonormal? What does it mean that matrix A is positive semi-definite? A is a matrix. What is the definition of its pseudoinverse?
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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only solve 2,3,4, theyre one question broken
Transcribed Image Text:Consider the matrix X and the vectors y and z below:
[2 4
X=
1 3
[1
[2
y=
Z=
3
3
a. What is the inner product of the vectors y and z? (this is also sometimes called the
dot product, and is sometimes written y"z)
b. What is the product Xy?
c. Is X invertible? If so, give the inverse, and if no, explain why not.
d. What is the rank of X? Explain your answer.
What does it mean that matrix A is orthonormal?
What does it mean that matrix A is positive semi-definite?
A is a matrix. What is the definition of its pseudoinverse?
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