Math Problem Statement
nilai a adalah
nilai a adalah
Solution
To solve the equation shown in the image, we equate corresponding elements from both matrices because the two matrices are equal. Let’s solve step by step:
The matrix equation is:
a + b & 2 - a \\ 9 & 5 - c \end{bmatrix} = \begin{bmatrix} b + a & 2a + 8 \\ 9 & -c + 5 \end{bmatrix}.$$ ### Step 1: Equate corresponding elements #### Top-left: $$a + b = b + a$$ This is true for any $$a$$ and $$b$$, so it doesn’t give us any new information. #### Top-right: $$2 - a = 2a + 8$$ Solve for $$a$$: $$2 - a = 2a + 8 \\ 2 = 2a + a + 8 \\ 2 = 3a + 8 \\ 3a = -6 \\ a = -2.$$ ### Step 2: Verify remaining equations #### Bottom-left: $$9 = 9$$ This is already satisfied. #### Bottom-right: $$5 - c = -c + 5$$ Simplify: $$5 - c = -c + 5 \\ 5 = 5 \quad \text{(true for any $$c$$)}.$$ ### Final Answer: $$a = -2.$$ Let me know if you'd like more explanation! ### Related Questions: 1. What are the values of $$b$$ and $$c$$ in this system? 2. How can matrices be equal in general terms? 3. What happens if one element in two matrices doesn’t match? 4. Can we solve for other variables ($$b, c$$) based on the given system? 5. What are the practical applications of solving such matrix equations? ### Tip: When working with equal matrices, always equate corresponding entries to set up equations!Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Matrix Equality
Algebra
Formulas
Equating corresponding elements of matrices
Theorems
Equality of Matrices
Suitable Grade Level
Grades 10-12
Related Recommendation
Matrix Equation: Solving for 'a' in Equality
Solving Matrix Equation for a and b in Matrix Equality
Solve for Variable a in a Matrix Equation: Step-by-Step Guide
Solving for Variables in Matrix Equality: a + b + c
Determine Parameter 'a' for Unique, Infinite, or No Solutions in a System of Linear Equations