Math Problem Statement
Jumlah dari semua elemen pada matriks: (5 7; -1 -5) + (-1 4; 2 -2) - (30 0; 0 0). Q adalah ....
Solution
I see an image with a matrix problem involving the summation of matrix elements. Let's break it down:
The given expression involves matrices:
5 & 7 \\ -1 & -5 \end{pmatrix} + \begin{pmatrix} -1 & 4 \\ 2 & -2 \end{pmatrix} - \begin{pmatrix} 30 & 0 \\ 0 & 0 \end{pmatrix}$$ We are tasked to find the sum of all elements after performing the matrix operations. Let's first compute the matrix sum and difference and then calculate the total sum of the elements.After performing the matrix operations: $$\begin{pmatrix} 5 & 7 \\ -1 & -5 \end{pmatrix} + \begin{pmatrix} -1 & 4 \\ 2 & -2 \end{pmatrix} - \begin{pmatrix} 30 & 0 \\ 0 & 0 \end{pmatrix} = \begin{pmatrix} -26 & 11 \\ 1 & -7 \end{pmatrix}$$ The sum of all the elements in the resulting matrix is: $$-26 + 11 + 1 - 7 = -21$$ Thus, the total sum is $$-21$$. Do you have any questions or would you like further details? Here are five related questions for further exploration: 1. How would you perform matrix addition and subtraction with 3x3 matrices? 2. Can matrices of different sizes be added or subtracted? 3. What is the geometric interpretation of matrix operations like addition or subtraction? 4. How would the result differ if we multiply instead of adding or subtracting matrices? 5. What are some real-life applications of matrix operations? **Tip:** When working with matrix operations, ensure that the matrices have the same dimensions for addition or subtraction.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Addition
Matrix Subtraction
Summation of Matrix Elements
Formulas
Matrix Addition: A + B = C, where A, B, and C are matrices of the same dimensions
Summation of Matrix Elements: Sum all elements in the resulting matrix after operations
Theorems
Matrix Addition and Subtraction: Matrices of the same dimensions can be added or subtracted element-wise.
Suitable Grade Level
Grades 9-11