Solve the matrix equation for Y. Simplify all elements.
9	5	9	1
 = 	
–
4	
–
4	0	
–
4
 –Y

We are given the matrix equation:

\[
\begin{bmatrix} 
9 & 5 & 9 & 1 
\end{bmatrix}
= 
\begin{bmatrix} 
-4 & -4 & 0 & -4 
\end{bmatrix} - Y
\]

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.

Solve the matrix equation for Y. Simplify all elements.

Learn how to solve the matrix equation for Y by simplifying all elements through matrix subtraction. This step-by-step solution includes key matrix operations concepts, ideal for high school students in Grades 10-12.

Math Problem Statement

Solve the matrix equation for Y. Simplify all elements. 9 5 9 1

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