**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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