Determine if the following operation on the two given matrices is defined, and if it is, determine the order of the resulting matrix. [4] [43] The result of the operation is defined defined undefined The order of the result is
Determine if the following operation on the two given matrices is defined, and if it is, determine the order of the resulting matrix. [4] [43] The result of the operation is defined defined undefined The order of the result is
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
Related questions
Question
![### Matrix Operation Determination
#### Task:
Determine if the following operation on the two given matrices is **defined**, and if it is, determine the order of the resulting matrix.
\[ [-4 \quad 4 \quad 3] \]
**Result Options:**
- The result of the operation is:
- **defined**
- **undefined**
- The order of the result is:
- input the relevant order or select the appropriate option
#### Instruction for Matrix Multiplication:
To determine if the operation between two matrices is defined, you need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
*Example:*
- For matrix \( A \) of order \( m \times n \) and matrix \( B \) of order \( p \times q \), the matrix multiplication \( AB \) is defined if \( n = p \).
- The resulting matrix \( AB \) will have the order \( m \times q \).
**Interactive Element:**
Students can select whether the operation is defined or undefined from the dropdown menu provided and, if defined, should input the resultant matrix's order.
This exercise is taken from DeltaMath student portal for better understanding and practice with matrix operations.
**Note:** Please apply matrix multiplication rules to determine the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faca5ab5d-d1b4-4091-b3ec-a6eaf8cb8003%2F8cd36ccf-b0eb-48a7-a885-19d5cdcca89f%2F297zgxr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Operation Determination
#### Task:
Determine if the following operation on the two given matrices is **defined**, and if it is, determine the order of the resulting matrix.
\[ [-4 \quad 4 \quad 3] \]
**Result Options:**
- The result of the operation is:
- **defined**
- **undefined**
- The order of the result is:
- input the relevant order or select the appropriate option
#### Instruction for Matrix Multiplication:
To determine if the operation between two matrices is defined, you need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
*Example:*
- For matrix \( A \) of order \( m \times n \) and matrix \( B \) of order \( p \times q \), the matrix multiplication \( AB \) is defined if \( n = p \).
- The resulting matrix \( AB \) will have the order \( m \times q \).
**Interactive Element:**
Students can select whether the operation is defined or undefined from the dropdown menu provided and, if defined, should input the resultant matrix's order.
This exercise is taken from DeltaMath student portal for better understanding and practice with matrix operations.
**Note:** Please apply matrix multiplication rules to determine the correct answer.
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