Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Matrix Multiplication Problem**
To find the entry (1, 1) of the matrix product \( XY \), we will use the matrices below:
\[
X = \begin{pmatrix}
a \\
b \\
1 \\
\end{pmatrix}
\quad \text{and} \quad
Y = \begin{pmatrix}
c & -1 & d \\
\end{pmatrix}
\]
We are given the values:
\[ a = -5, \; b = 5, \; c = 7, \; \text{and} \; d = 1 \]
**Step-by-Step Solution:**
1. First, substitute the given values into the matrices \( X \) and \( Y \):
\[
X = \begin{pmatrix}
-5 \\
5 \\
1 \\
\end{pmatrix}
\quad \text{and} \quad
Y = \begin{pmatrix}
7 & -1 & 1 \\
\end{pmatrix}
\]
2. Perform the matrix multiplication \( XY \) to find the (1, 1) entry. The (1, 1) entry of the product \( XY \) is obtained by summing the products of corresponding entries from the first row of \( X \) and the first column of \( Y \):
\[
XY = (-5 \times 7) + (5 \times -1) + (1 \times 1)
\]
3. Calculate the products and their sum:
\[
XY = (-35) + (-5) + 1 = -35 - 5 + 1 = -39
\]
Therefore, the (1, 1) entry of the matrix product \( XY \) is \( -39 \).
**Final Answer:**
Enter your answer as a whole number. For example: 23 or 135 or 8.
\[
\boxed{-39}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9cf31a2-48b9-479e-8ba8-2adc6c3b60d9%2F34290a27-fe91-449a-8ad1-07b183eab036%2Fevaavq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplication Problem**
To find the entry (1, 1) of the matrix product \( XY \), we will use the matrices below:
\[
X = \begin{pmatrix}
a \\
b \\
1 \\
\end{pmatrix}
\quad \text{and} \quad
Y = \begin{pmatrix}
c & -1 & d \\
\end{pmatrix}
\]
We are given the values:
\[ a = -5, \; b = 5, \; c = 7, \; \text{and} \; d = 1 \]
**Step-by-Step Solution:**
1. First, substitute the given values into the matrices \( X \) and \( Y \):
\[
X = \begin{pmatrix}
-5 \\
5 \\
1 \\
\end{pmatrix}
\quad \text{and} \quad
Y = \begin{pmatrix}
7 & -1 & 1 \\
\end{pmatrix}
\]
2. Perform the matrix multiplication \( XY \) to find the (1, 1) entry. The (1, 1) entry of the product \( XY \) is obtained by summing the products of corresponding entries from the first row of \( X \) and the first column of \( Y \):
\[
XY = (-5 \times 7) + (5 \times -1) + (1 \times 1)
\]
3. Calculate the products and their sum:
\[
XY = (-35) + (-5) + 1 = -35 - 5 + 1 = -39
\]
Therefore, the (1, 1) entry of the matrix product \( XY \) is \( -39 \).
**Final Answer:**
Enter your answer as a whole number. For example: 23 or 135 or 8.
\[
\boxed{-39}
\]
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