Select The Correct Answer From The Drop-down Menu.${ A=\begin{bmatrix} -9 \ 0 \ 3 \ -1 \end{bmatrix}, \quad B=\begin{bmatrix} 0 \ 4 \ -6 \ 2 \end{bmatrix} }$The Order Of Matrix { A + B $}$ Is { \square$}$.

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Introduction to Matrix Addition

In mathematics, matrices are used to represent systems of linear equations and perform various operations. One of the fundamental operations in matrix algebra is addition. Matrix addition is a straightforward process where two matrices are added element-wise. However, before we dive into the details of matrix addition, it's essential to understand the concept of the order of a matrix.

What is the Order of a Matrix?

The order of a matrix is defined as the number of rows and columns it contains. For example, a matrix with 3 rows and 4 columns has an order of 3x4. The order of a matrix is crucial in determining the validity of matrix operations, including addition.

Matrix Addition

Given two matrices A and B, the sum of A and B is denoted as A + B. The resulting matrix has the same order as the original matrices. To add two matrices, we simply add the corresponding elements of the two matrices.

Example: Adding Matrices A and B

Let's consider the matrices A and B given in the problem statement:

A=\begin{bmatrix} -9 \ 0 \ 3 \ -1 \end{bmatrix}, \quad B=\begin{bmatrix} 0 \ 4 \ -6 \ 2 \end{bmatrix}

To add these matrices, we simply add the corresponding elements:

A + B = \begin{bmatrix} -9 + 0 \ 0 + 4 \ 3 + (-6) \ -1 + 2 \end{bmatrix} = \begin{bmatrix} -9 \ 4 \ -3 \ 1 \end{bmatrix}

Determining the Order of the Resulting Matrix

Now that we have added the matrices A and B, we need to determine the order of the resulting matrix. Since both matrices A and B have 4 rows, the resulting matrix A + B also has 4 rows. Similarly, since both matrices A and B have 1 column, the resulting matrix A + B also has 1 column.

Therefore, the order of the matrix A + B is 4x1.

Conclusion

In this article, we discussed the concept of matrix addition and the order of matrices. We learned that matrix addition is a straightforward process where two matrices are added element-wise, and the resulting matrix has the same order as the original matrices. We also saw an example of adding two matrices and determined the order of the resulting matrix.

Key Takeaways

  • Matrix addition is a fundamental operation in matrix algebra.
  • The order of a matrix is defined as the number of rows and columns it contains.
  • The order of the resulting matrix is the same as the original matrices.
  • Matrix addition is a straightforward process where two matrices are added element-wise.

Frequently Asked Questions

  • What is the order of a matrix?
  • How do you add two matrices?
  • What is the order of the resulting matrix after adding two matrices?

Answer Key

  • The order of a matrix is defined as the number of rows and columns it contains.
  • To add two matrices, you simply add the corresponding elements of the two matrices.
  • The order of the resulting matrix is the same as the original matrices.
    Matrix Addition and Order of Matrices: Q&A =====================================

Introduction

In our previous article, we discussed the concept of matrix addition and the order of matrices. We learned that matrix addition is a fundamental operation in matrix algebra, and the order of a matrix is defined as the number of rows and columns it contains. In this article, we will answer some frequently asked questions related to matrix addition and order of matrices.

Q&A

Q: What is the order of a matrix?

A: The order of a matrix is defined as the number of rows and columns it contains. For example, a matrix with 3 rows and 4 columns has an order of 3x4.

Q: How do you add two matrices?

A: To add two matrices, you simply add the corresponding elements of the two matrices. For example, if we have two matrices A and B, the sum of A and B is denoted as A + B, and is calculated as:

A + B = \begin{bmatrix} a_{11} + b_{11} & a_{12} + b_{12} \ a_{21} + b_{21} & a_{22} + b_{22} \end{bmatrix}

Q: What is the order of the resulting matrix after adding two matrices?

A: The order of the resulting matrix is the same as the original matrices. In other words, if we have two matrices A and B with orders m x n and p x q, respectively, the order of the resulting matrix A + B is also m x n.

Q: Can we add two matrices if they have different orders?

A: No, we cannot add two matrices if they have different orders. The order of the resulting matrix must be the same as the original matrices.

Q: What happens if we try to add two matrices with different orders?

A: If we try to add two matrices with different orders, the operation is undefined. In other words, we cannot perform matrix addition on two matrices with different orders.

Q: Can we add a matrix to a scalar?

A: Yes, we can add a matrix to a scalar. In this case, the scalar is added to each element of the matrix.

Q: What is the order of the resulting matrix after adding a matrix to a scalar?

A: The order of the resulting matrix is the same as the original matrix.

Q: Can we add a scalar to a matrix if the scalar is a matrix?

A: No, we cannot add a scalar to a matrix if the scalar is a matrix. The scalar must be a number, not a matrix.

Q: What is the difference between matrix addition and scalar multiplication?

A: Matrix addition is the process of adding two matrices, while scalar multiplication is the process of multiplying a matrix by a scalar.

Q: Can we perform matrix addition and scalar multiplication on the same matrix?

A: Yes, we can perform matrix addition and scalar multiplication on the same matrix. However, we must be careful to follow the correct order of operations.

Conclusion

In this article, we answered some frequently asked questions related to matrix addition and order of matrices. We learned that matrix addition is a fundamental operation in matrix algebra, and the order of a matrix is defined as the number of rows and columns it contains. We also discussed the rules for adding matrices, including the order of the resulting matrix and the possibility of adding matrices with different orders.

Key Takeaways

  • Matrix addition is a fundamental operation in matrix algebra.
  • The order of a matrix is defined as the number of rows and columns it contains.
  • The order of the resulting matrix is the same as the original matrices.
  • We cannot add two matrices if they have different orders.
  • We can add a matrix to a scalar, but not a scalar to a matrix if the scalar is a matrix.

Frequently Asked Questions

  • What is the order of a matrix?
  • How do you add two matrices?
  • What is the order of the resulting matrix after adding two matrices?
  • Can we add two matrices if they have different orders?
  • What happens if we try to add two matrices with different orders?

Answer Key

  • The order of a matrix is defined as the number of rows and columns it contains.
  • To add two matrices, you simply add the corresponding elements of the two matrices.
  • The order of the resulting matrix is the same as the original matrices.
  • No, we cannot add two matrices if they have different orders.
  • If we try to add two matrices with different orders, the operation is undefined.