Find `X` if `Y=[3, 2, 1 ,4]` and `2X+Y=[1, 0, -3, 2]` .

Explanation

To find the matrix \( X \) given that \( Y = [3, 2, 1, 4] \) and \( 2X + Y = [1, 0, -3, 2] \), we will follow these steps:

### Step 1: Substitute the value of \( Y \) into the equation
We start with the equation:
\[ 2X + Y = [1, 0, -3, 2] \]
Substituting \( Y = [3, 2, 1, 4] \):
\[ 2X + [3, 2, 1, 4] = [1, 0, -3, 2] \]

### Step 2: Rearrange the equation to isolate \( 2X \)
To isolate \( 2X \), we subtract \( Y \) from both sides:
\[ 2X = [1, 0, -3, 2] - [3, 2, 1, 4] \]

### Step 3: Perform the subtraction
Now, we perform the subtraction element-wise:
\[ 2X = [1 - 3, 0 - 2, -3 - 1, 2 - 4] \]
This simplifies to:
\[ 2X = [-2, -2, -4, -2] \]

### Step 4: Divide by 2 to solve for \( X \)
Now, we divide each element of \( 2X \) by 2 to find \( X \):
\[ X = \left[-2/2, -2/2, -4/2, -2/2\right] \]
This simplifies to:
\[ X = [-1, -1, -2, -1] \]

### Final Answer
Thus, the matrix \( X \) is:
\[ X = [-1, -1, -2, -1] \]