Question

If \( \begin{pmatrix} 1 & 2 & -3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \), then \( (x, y, z) \) is equal to:

• A. \( (1, 6, 6) \)
• B. \( (1, -6, 1) \)
• C. \( (1, 1, 6) \)
• D. \( (6, -1, 1) \)
• E. \( (-1, 6, 1) \)

Hint:

Always check the diagonal of the matrix. If all entries below the diagonal are zero, start solving from the last variable. It avoids the need for complex matrix inversion.

Answer 1

The Correct Option is D