1. Vectors and Matrices: Consider the matrix X and the vectors y and z below: [2 4] X= 2 3 y= Z= 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? no, c. Is X invertible? If so, give the inverse, and if explain why not. d. What is the rank of X? Explain your answer.

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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see attached. its one full question but broken into several questions.

1. Vectors and Matrices:
Consider the matrix X and the vectors y and z below:
x- - -|
[2 4
X=
1 3
2
y=
Z=
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.
Transcribed Image Text:1. Vectors and Matrices: Consider the matrix X and the vectors y and z below: x- - -| [2 4 X= 1 3 2 y= Z= 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.
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