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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![### Matrix Multiplication Example
In this example, we are given two matrices that we need to multiply:
\[
\begin{bmatrix}
-7 & -9 & -6 \\
0 & -4 & -6 \\
0 & 0 & -9
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
5 & 8 & 4 \\
0 & 5 & -3 \\
0 & 0 & 6
\end{bmatrix}
\]
We need to find the product of these matrices and fill in the resulting matrix.
The corresponding empty matrix for the result is indicated as:
\[
\begin{bmatrix}
& & \\
& & \\
& &
\end{bmatrix}
\]
To compute each element of the resulting matrix, remember to take the dot product of rows from the first matrix with columns from the second matrix. For instance:
- The element in the first row and first column of the resulting matrix is computed by:
\[(-7 \times 5) + (-9 \times 0) + (-6 \times 0)\]
- Continue similarly for other elements.
By solving these, we'll fill in the empty matrix step by step.
### Step-by-step Calculation:
1. **First Row, First Column:**
\[(-7 \times 5) + (-9 \times 0) + (-6 \times 0) = -35\]
2. **First Row, Second Column:**
\[(-7 \times 8) + (-9 \times 5) + (-6 \times 0) = -56 + -45 = -101\]
3. **First Row, Third Column:**
\[(-7 \times 4) + (-9 \times -3) + (-6 \times 6) = -28 + 27 + -36 = -37\]
Continue with the same approach for the other rows and columns to fill the entire result matrix.
#### Suggestions for Visual Aid
- Use an online matrix multiplication calculator for verification.
- Practice multiplying small matrices by hand to understand the step-by-step procedure.
### Filled Resulting Matrix
\[
\begin{bmatrix}
-35 & -101 & -37 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e366a85-c23b-450a-9bc7-d2ea0be52d3f%2F36b5207f-290a-48ac-a0d7-de0142686199%2F31j75f_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Multiplication Example
In this example, we are given two matrices that we need to multiply:
\[
\begin{bmatrix}
-7 & -9 & -6 \\
0 & -4 & -6 \\
0 & 0 & -9
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
5 & 8 & 4 \\
0 & 5 & -3 \\
0 & 0 & 6
\end{bmatrix}
\]
We need to find the product of these matrices and fill in the resulting matrix.
The corresponding empty matrix for the result is indicated as:
\[
\begin{bmatrix}
& & \\
& & \\
& &
\end{bmatrix}
\]
To compute each element of the resulting matrix, remember to take the dot product of rows from the first matrix with columns from the second matrix. For instance:
- The element in the first row and first column of the resulting matrix is computed by:
\[(-7 \times 5) + (-9 \times 0) + (-6 \times 0)\]
- Continue similarly for other elements.
By solving these, we'll fill in the empty matrix step by step.
### Step-by-step Calculation:
1. **First Row, First Column:**
\[(-7 \times 5) + (-9 \times 0) + (-6 \times 0) = -35\]
2. **First Row, Second Column:**
\[(-7 \times 8) + (-9 \times 5) + (-6 \times 0) = -56 + -45 = -101\]
3. **First Row, Third Column:**
\[(-7 \times 4) + (-9 \times -3) + (-6 \times 6) = -28 + 27 + -36 = -37\]
Continue with the same approach for the other rows and columns to fill the entire result matrix.
#### Suggestions for Visual Aid
- Use an online matrix multiplication calculator for verification.
- Practice multiplying small matrices by hand to understand the step-by-step procedure.
### Filled Resulting Matrix
\[
\begin{bmatrix}
-35 & -101 & -37 \
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