[B] = -5 -11 18 -10 0 -14 14 -12 13 5 -16 -8 17 9 12 -17 If matrix [B] has element brc = −10, what is r and c? TH and c=
[B] = -5 -11 18 -10 0 -14 14 -12 13 5 -16 -8 17 9 12 -17 If matrix [B] has element brc = −10, what is r and c? TH and c=
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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Question
![## Understanding Matrices
In the study of linear algebra, a matrix is a rectangular array of numbers arranged in rows and columns. Matrices are used to represent linear equations and transformations.
### Problem Statement
Consider the matrix \([B]\) given below:
\[
[B] =
\begin{bmatrix}
-5 & -11 & 18 & -10 \\
0 & -14 & 14 & -12 \\
13 & 5 & -16 & -8 \\
-17 & 17 & 9 & 12
\end{bmatrix}
\]
We are interested to know the position \((r, c)\) of the element \(-10\) in this matrix. The notation \(b_{rc}\) represents the element located in the \(r\)-th row and \(c\)-th column of the matrix \([B]\).
### Question
If matrix \([B]\) has element \(b_{rc} = -10\), what are the values of \(r\) and \(c\)?
### Solution
To find the specific position \((r, c)\) of the element \(-10\) in the matrix \([B]\), you need to inspect each element in the matrix and find its corresponding row and column indices.
1. **First Row**: \((-5)\, (-11)\, (18)\, \(\underline{-10}\))
2. **Second Row**: \((0)\, (-14)\, (14)\, (-12)\)
3. **Third Row**: \((13)\, (5)\, (-16)\, (-8)\)
4. **Fourth Row**: \((-17)\, (17)\, (9)\, (12)\)
In the first row, you can see that \(-10\) is positioned at the 4th column.
Hence, \(r = 1\) and \(c = 4\).
```
r = __1__ and c = __4__
```
Feel free to click "Check Answer" to verify your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F4222485f-faa5-4331-9f94-fa650373dce5%2Fq3qdz8k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Understanding Matrices
In the study of linear algebra, a matrix is a rectangular array of numbers arranged in rows and columns. Matrices are used to represent linear equations and transformations.
### Problem Statement
Consider the matrix \([B]\) given below:
\[
[B] =
\begin{bmatrix}
-5 & -11 & 18 & -10 \\
0 & -14 & 14 & -12 \\
13 & 5 & -16 & -8 \\
-17 & 17 & 9 & 12
\end{bmatrix}
\]
We are interested to know the position \((r, c)\) of the element \(-10\) in this matrix. The notation \(b_{rc}\) represents the element located in the \(r\)-th row and \(c\)-th column of the matrix \([B]\).
### Question
If matrix \([B]\) has element \(b_{rc} = -10\), what are the values of \(r\) and \(c\)?
### Solution
To find the specific position \((r, c)\) of the element \(-10\) in the matrix \([B]\), you need to inspect each element in the matrix and find its corresponding row and column indices.
1. **First Row**: \((-5)\, (-11)\, (18)\, \(\underline{-10}\))
2. **Second Row**: \((0)\, (-14)\, (14)\, (-12)\)
3. **Third Row**: \((13)\, (5)\, (-16)\, (-8)\)
4. **Fourth Row**: \((-17)\, (17)\, (9)\, (12)\)
In the first row, you can see that \(-10\) is positioned at the 4th column.
Hence, \(r = 1\) and \(c = 4\).
```
r = __1__ and c = __4__
```
Feel free to click "Check Answer" to verify your solution.
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