9. The set of all 2 x 2 matrices of the form 07 0 b] with the standard matrix addition and scalar multiplication.
9. The set of all 2 x 2 matrices of the form 07 0 b] with the standard matrix addition and scalar multiplication.
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
Showthat the closure axioms ( 1and 6) and the
axioms for the zero vector (4) and the negative
vector (5) all hold
![**9. The set of all \(2 \times 2\) matrices of the form**
\[
\begin{bmatrix}
a & 0 \\
0 & b
\end{bmatrix}
\]
**with the standard matrix addition and scalar multiplication.**
**Explanation:**
This entry describes a specific type of \(2 \times 2\) matrix known as a diagonal matrix. In this form, all the non-diagonal elements are zero. The variables \(a\) and \(b\) can be any real numbers, representing the elements on the main diagonal.
**Operations:**
- **Matrix Addition:** When adding two matrices of this type, the resulting matrix will have diagonal elements which are the sums of the corresponding diagonal elements of the two matrices.
- **Scalar Multiplication:** When multiplying a matrix by a scalar, each element in the matrix, including both diagonals, is multiplied by that scalar. The zero elements remain unchanged.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78fa799e-dd0d-498f-bbc7-16121e7aabca%2F4e08173e-2415-46ba-a874-22c5e80342c5%2Fn9md1fq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**9. The set of all \(2 \times 2\) matrices of the form**
\[
\begin{bmatrix}
a & 0 \\
0 & b
\end{bmatrix}
\]
**with the standard matrix addition and scalar multiplication.**
**Explanation:**
This entry describes a specific type of \(2 \times 2\) matrix known as a diagonal matrix. In this form, all the non-diagonal elements are zero. The variables \(a\) and \(b\) can be any real numbers, representing the elements on the main diagonal.
**Operations:**
- **Matrix Addition:** When adding two matrices of this type, the resulting matrix will have diagonal elements which are the sums of the corresponding diagonal elements of the two matrices.
- **Scalar Multiplication:** When multiplying a matrix by a scalar, each element in the matrix, including both diagonals, is multiplied by that scalar. The zero elements remain unchanged.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
