Find The Product.$\[ \left[\begin{array}{ll} -4 & 4 \end{array}\right] \left[\begin{array}{rrr} -2 & -9 & 7 \\ 4 & 8 & 3 \end{array}\right] \\]
Introduction
In mathematics, matrix multiplication is a fundamental operation that allows us to combine two or more matrices to produce a new matrix. This operation is used extensively in various fields, including linear algebra, calculus, and computer science. In this article, we will focus on finding the product of two matrices, specifically the product of a 1x2 matrix and a 2x3 matrix.
Matrix Multiplication Rules
Before we dive into the problem, let's review the rules of matrix multiplication. Matrix multiplication is only possible when the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, we have a 1x2 matrix and a 2x3 matrix, so the multiplication is possible.
The Product of Two Matrices
The product of two matrices A and B is denoted as AB and is calculated by multiplying the elements of each row of matrix A with the elements of each column of matrix B.
Step 1: Multiply the First Row of Matrix A with the First Column of Matrix B
To find the first element of the product matrix, we multiply the first row of matrix A with the first column of matrix B.
[-4 4]
[-2 -9 7]
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<br/>
**Matrix Multiplication: A Q&A Guide**
=====================================
**Introduction**
---------------
Matrix multiplication is a fundamental concept in linear algebra, and it's used extensively in various fields, including computer science, physics, and engineering. However, it can be a bit tricky to understand, especially for beginners. In this article, we'll provide a Q&A guide to help you understand matrix multiplication better.
**Q: What is matrix multiplication?**
--------------------------------------
A: Matrix multiplication is a mathematical operation that combines two or more matrices to produce a new matrix. It's a way of multiplying the elements of each row of the first matrix with the elements of each column of the second matrix.
**Q: What are the rules of matrix multiplication?**
------------------------------------------------
A: The rules of matrix multiplication are as follows:
* The number of columns in the first matrix must be equal to the number of rows in the second matrix.
* The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
* Each element of the resulting matrix is calculated by multiplying the elements of each row of the first matrix with the elements of each column of the second matrix.
**Q: How do I multiply two matrices?**
--------------------------------------
A: To multiply two matrices, you need to follow these steps:
1. Check if the matrices can be multiplied. If the number of columns in the first matrix is not equal to the number of rows in the second matrix, they cannot be multiplied.
2. Create a new matrix with the same number of rows as the first matrix and the same number of columns as the second matrix.
3. Multiply the elements of each row of the first matrix with the elements of each column of the second matrix.
4. Place the results in the corresponding position in the new matrix.
**Q: What is the product of a 1x2 matrix and a 2x3 matrix?**
------------------------------------------------------
A: To find the product of a 1x2 matrix and a 2x3 matrix, we need to multiply the elements of each row of the 1x2 matrix with the elements of each column of the 2x3 matrix.
```markdown
[-4 4]
[-2 -9 7]
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