Compute the indicated product. -1 5 34 01 2 1 2 325
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
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![## Matrix Multiplication Problem
**Compute the indicated product:**
\[
\begin{pmatrix}
-1 & 5 & 0 \\
3 & 4 & 1 \\
0 & 1 & 0
\end{pmatrix}
\begin{pmatrix}
2 & 1 & 2 \\
1 & 2 & 5 \\
3 & 2 & 5
\end{pmatrix}
\]
**Explanation of the Diagram:**
The diagram shows two matrices, where the objective is to compute their product. Below the matrices, there is a blank 3x3 matrix (represented by empty boxes) indicating the placeholders for the resulting matrix after performing the multiplication. Green arrows point downwards and to the right, indicating the direction for applying the matrix multiplication operations.
For each element in the resulting matrix, you perform the dot product of the corresponding row from the first matrix with the column from the second matrix.
**Steps to Compute the Product:**
1. **Element at (1,1):**
\[ (-1 * 2) + (5 * 1) + (0 * 3) = -2 + 5 + 0 = 3 \]
2. **Element at (1,2):**
\[ (-1 * 1) + (5 * 2) + (0 * 2) = -1 + 10 + 0 = 9 \]
3. **Element at (1,3):**
\[ (-1 * 2) + (5 * 5) + (0 * 5) = -2 + 25 + 0 = 23 \]
4. **Element at (2,1):**
\[ (3 * 2) + (4 * 1) + (1 * 3) = 6 + 4 + 3 = 13 \]
5. **Element at (2,2):**
\[ (3 * 1) + (4 * 2) + (1 * 2) = 3 + 8 + 2 = 13 \]
6. **Element at (2,3):**
\[ (3 * 2) + (4 * 5) + (1 * 5) = 6 + 20 + 5 = 31](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77247d15-844d-4e77-b205-212be8c6419e%2F469feea1-1c69-4db3-ab12-4d350c592302%2F7v1s4o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Matrix Multiplication Problem
**Compute the indicated product:**
\[
\begin{pmatrix}
-1 & 5 & 0 \\
3 & 4 & 1 \\
0 & 1 & 0
\end{pmatrix}
\begin{pmatrix}
2 & 1 & 2 \\
1 & 2 & 5 \\
3 & 2 & 5
\end{pmatrix}
\]
**Explanation of the Diagram:**
The diagram shows two matrices, where the objective is to compute their product. Below the matrices, there is a blank 3x3 matrix (represented by empty boxes) indicating the placeholders for the resulting matrix after performing the multiplication. Green arrows point downwards and to the right, indicating the direction for applying the matrix multiplication operations.
For each element in the resulting matrix, you perform the dot product of the corresponding row from the first matrix with the column from the second matrix.
**Steps to Compute the Product:**
1. **Element at (1,1):**
\[ (-1 * 2) + (5 * 1) + (0 * 3) = -2 + 5 + 0 = 3 \]
2. **Element at (1,2):**
\[ (-1 * 1) + (5 * 2) + (0 * 2) = -1 + 10 + 0 = 9 \]
3. **Element at (1,3):**
\[ (-1 * 2) + (5 * 5) + (0 * 5) = -2 + 25 + 0 = 23 \]
4. **Element at (2,1):**
\[ (3 * 2) + (4 * 1) + (1 * 3) = 6 + 4 + 3 = 13 \]
5. **Element at (2,2):**
\[ (3 * 1) + (4 * 2) + (1 * 2) = 3 + 8 + 2 = 13 \]
6. **Element at (2,3):**
\[ (3 * 2) + (4 * 5) + (1 * 5) = 6 + 20 + 5 = 31
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