Performing Matrix Subtraction

Oct 13, 2025 by windailys.com 66 views

Introduction

Matrix subtraction is a fundamental operation in linear algebra, where two matrices are subtracted element-wise. In this article, we will explore the values of c and d in the matrix subtraction below.

Matrix Subtraction

The given matrix subtraction is:

\begin{bmatrix} c+2 &amp; 3 \\ -5 &amp; d-4 \end{bmatrix}

\begin{bmatrix} 22 & 5 \ -6 & }$

To find the values of c and d, we need to perform the matrix subtraction and equate the corresponding elements.

Performing Matrix Subtraction

Let's perform the matrix subtraction:

{ \begin{bmatrix} 6 &amp; 8 \\ -11 &amp; 15 \end{bmatrix} - \begin{bmatrix} c+2 &amp; 3 \\ -5 &amp; d-4 \end{bmatrix} = \begin{bmatrix} 6 - (c+2) &amp; 8 - 3 \\ -11 - (-5) &amp; 15 - (d-4) \end{bmatrix} = \begin{bmatrix} 6 - c - 2 &amp; 5 \\ -6 &amp; 19 - d + 4 \end{bmatrix} = \begin{bmatrix} 4 - c &amp; 5 \\ -6 &amp; 23 - d \end{bmatrix} }$ **Equating Corresponding Elements** ---------------------------------- Now, we can equate the corresponding elements of the resulting matrix with the given matrix: $${ \begin{bmatrix} 4 - c &amp; 5 \\ -6 &amp; 23 - d \end{bmatrix} = \begin{bmatrix} 22 &amp; 5 \\ -6 &amp; }$ Equating the elements in the first row, we get: 4 - c = 22 ... (1) Equating the elements in the second row, we get: -6 = -6 ... (2) Equating the elements in the first column, we get: -6 = -6 ... (3) Equating the elements in the second column, we get: 23 - d = 5 ... (4) **Solving for c and d** ------------------------- Now, we can solve for c and d using the equations (1), (2), (3), and (4). From equation (1), we can solve for c: 4 - c = 22 c = 4 - 22 c = -18 From equation (4), we can solve for d: 23 - d = 5 d = 23 - 5 d = 18 **Conclusion** -------------- In this article, we have found the values of c and d in the matrix subtraction below. The values of c and d are -18 and 18, respectively. **Final Answer** ---------------- The final answer is: c = -18 d = 18&lt;br/&gt; **Matrix Subtraction: Q&amp;A** ========================== **Introduction** --------------- In our previous article, we explored the values of c and d in the matrix subtraction below. In this article, we will answer some frequently asked questions related to matrix subtraction. **Q: What is matrix subtraction?** ------------------------------- A: Matrix subtraction is a fundamental operation in linear algebra, where two matrices are subtracted element-wise. It is denoted by the symbol `-` and is used to find the difference between two matrices. **Q: How do I perform matrix subtraction?** ----------------------------------------- A: To perform matrix subtraction, you need to subtract the corresponding elements of the two matrices. For example, if you have two matrices: $${ \begin{bmatrix} a &amp; b \\ c &amp; d \end{bmatrix} }$ and $${ \begin{bmatrix} e &amp; f \\ g &amp; h \end{bmatrix} }$ then the matrix subtraction would be: $${ \begin{bmatrix} a - e &amp; b - f \\ c - g &amp; d - h \end{bmatrix} }$ **Q: What are the rules for matrix subtraction?** -------------------------------------------- A: The rules for matrix subtraction are: * The matrices must have the same dimensions (i.e., the same number of rows and columns). * The corresponding elements of the two matrices must be subtracted element-wise. * The resulting matrix will have the same dimensions as the original matrices. **Q: Can I subtract a matrix from a scalar?** -------------------------------------------- A: No, you cannot subtract a matrix from a scalar. Matrix subtraction is only defined for matrices with the same dimensions. **Q: Can I subtract a matrix from a vector?** -------------------------------------------- A: No, you cannot subtract a matrix from a vector. Matrix subtraction is only defined for matrices with the same dimensions. **Q: What is the difference between matrix subtraction and matrix addition?** ------------------------------------------------------------------- A: Matrix subtraction and matrix addition are both operations that involve combining two matrices. However, matrix subtraction involves subtracting the corresponding elements of the two matrices, while matrix addition involves adding the corresponding elements of the two matrices. **Q: Can I use matrix subtraction to find the difference between two matrices?** ------------------------------------------------------------------- A: Yes, you can use matrix subtraction to find the difference between two matrices. This is a common application of matrix subtraction in linear algebra. **Q: Can I use matrix subtraction to find the sum of two matrices?** ---------------------------------------------------------------- A: No, you cannot use matrix subtraction to find the sum of two matrices. To find the sum of two matrices, you need to use matrix addition. **Conclusion** -------------- In this article, we have answered some frequently asked questions related to matrix subtraction. We hope that this article has been helpful in clarifying the rules and applications of matrix subtraction. **Final Answer** ---------------- The final answer is: Matrix subtraction is a fundamental operation in linear algebra that involves subtracting the corresponding elements of two matrices. **Common Mistakes** ------------------- * Subtracting a matrix from a scalar or a vector. * Subtracting two matrices with different dimensions. * Using matrix subtraction to find the sum of two matrices. **Tips and Tricks** ------------------- * Make sure to check the dimensions of the matrices before performing matrix subtraction. * Use matrix subtraction to find the difference between two matrices. * Use matrix addition to find the sum of two matrices.</span></p>