Math Problem Statement
Tentukan nilai a dan b Kesamaan matrik: \[\begin{bmatrix} a & -5 \\ 3 & -b \end{bmatrix} = \begin{bmatrix} 2a & -11 \\ b & +9 \end{bmatrix}\]
Solution
The problem is asking to determine the values of and from the following matrix equation:
a & -5 \\ 3 & -b \end{bmatrix} = \begin{bmatrix} 2a & -11 \\ b & +9 \end{bmatrix}$$ To solve for $$a$$ and $$b$$, we can equate the corresponding elements of the two matrices. This gives us the following system of equations: 1. $$a = 2a$$ (from the top-left elements) 2. $$-5 = -11$$ (from the top-right elements) 3. $$3 = b$$ (from the bottom-left elements) 4. $$-b = 9$$ (from the bottom-right elements) ### Solving these equations: 1. From $$a = 2a$$, subtract $$a$$ from both sides: $$0 = a$$ So, $$a = 0$$. 2. $$-5 = -11$$ is a contradiction, so this equation does not hold, meaning there is no solution. The given matrix equality is inconsistent. Thus, this system has **no solution** due to the contradictory equation $$-5 = -11$$. Would you like more details or have any questions? ### Related Questions: 1. What is a matrix equation? 2. Can matrix equations have no solutions or infinite solutions? 3. How can I determine the solution set for a matrix equation? 4. What methods can I use to solve a system of matrix equations? 5. Can matrices of different sizes be equated? **Tip:** When solving matrix equations, always check if the equations derived from corresponding elements are consistent.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Equations
Algebra
Formulas
Matrix equality rule: corresponding elements must be equal
Theorems
Matrix Equation Theorem: Equal matrices have equal corresponding elements
Suitable Grade Level
Grades 9-11