**Matrix Multiplication Problem**To find the entry (1, 1) of the matrix product \( XY \), we will use the matrices below:\[X = \begin{pmatrix}a \\b \\1 \\\end{pmatrix}\quad \text{and} \quadY = \begin{pmatrix}c & -1 & d \\\end{pmatrix}\]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 \( Y \):\[X = \begin{pmatrix}-5 \\5 \\1 \\\end{pmatrix}\quad \text{and} \quadY = \begin{pmatrix}7 & -1 & 1 \\\end{pmatrix}\]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.\[\boxed{-39}\]

To find entry of the matrix product using the the matrices below. and and , and .

Answered: Find the (1, 1) entry of the matrix…

Find the (1, 1) entry of the matrix product XY using the matrices below: a X = b and Y = | c 1 -1 d and where a = 5, b = 5, c = 7, and d = 1

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.

\[
\boxed{-39}
\]

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