Math Problem Statement
Solve the matrix equation for Y. Simplify all elements. 9 5 9 1
– 4 – 4 0 – 4 –Y
Solution
We are given the matrix equation:
9 & 5 & 9 & 1 \end{bmatrix} = \begin{bmatrix} -4 & -4 & 0 & -4 \end{bmatrix} - Y$$ We need to solve for $$Y$$ and simplify all elements. ### Step 1: Rearrange the equation to isolate $$Y$$ We can start by moving the matrix on the right-hand side to the other side: $$Y = \begin{bmatrix} -4 & -4 & 0 & -4 \end{bmatrix} - \begin{bmatrix} 9 & 5 & 9 & 1 \end{bmatrix}$$ ### Step 2: Subtract the matrices element-wise To perform the subtraction, subtract corresponding elements: $$Y = \begin{bmatrix} -4 - 9 & -4 - 5 & 0 - 9 & -4 - 1 \end{bmatrix}$$ This gives: $$Y = \begin{bmatrix} -13 & -9 & -9 & -5 \end{bmatrix}$$ Thus, the solution for $$Y$$ is: $$Y = \begin{bmatrix} -13 & -9 & -9 & -5 \end{bmatrix}$$ ### Do you need any further explanations or details? Here are some related questions you may find helpful: 1. What is the inverse of a matrix and how is it used in solving matrix equations? 2. How can matrix operations like addition, subtraction, and multiplication be applied in real-world problems? 3. What are the different methods to solve systems of equations using matrices? 4. How do you check the consistency of a matrix equation? 5. What are some properties of matrix addition and subtraction that you should always keep in mind? **Tip**: When performing matrix operations, remember that they are always done element-wise (row-by-row, column-by-column) for addition and subtraction.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Operations
Matrix Subtraction
Formulas
Matrix subtraction: A - B = C, where elements are subtracted element-wise
Theorems
Matrix subtraction theorem
Suitable Grade Level
Grades 10-12