If `A=[(-3,5,-8),(x,5,5),(0,y,4)]` is upper triangular matrix, then x+y is:

Options

A. 3
B. `-3`
C. 0
D. 1

Answer

To determine the values of \( x \) and \( y \) in the matrix \( A = \begin{pmatrix} -3 & 5 & -8 \\ x & 5 & 5 \\ 0 & y & 4 \end{pmatrix} \) such that \( A \) is an upper triangular matrix, we need to follow these steps:

### Step 1: Understand the Definition of an Upper Triangular Matrix
An upper triangular matrix is one where all the elements below the main diagonal are zero. For a 3x3 matrix, this means that the elements in positions (2,1), (3,1), and (3,2) must be zero.

### Step 2: Identify the Positions in the Matrix
In the matrix \( A \):
- The element at position (2,1) is \( x \).
- The element at position (3,1) is \( 0 \) (already zero).
- The element at position (3,2) is \( y \).

### Step 3: Set the Conditions for \( x \) and \( y \)
Since \( A \) is an upper triangular matrix:
- For the position (2,1) to be zero, we must have \( x = 0 \).
- For the position (3,2) to be zero, we must have \( y = 0 \).

### Step 4: Calculate \( x + y \)
Now that we have determined the values:
- \( x = 0 \)
- \( y = 0 \)

We can calculate:
\[ x + y = 0 + 0 = 0 \]

### Conclusion
Thus, the value of \( x + y \) is \( 0 \).