Question

If the system of linear equations:
\[ 2x + y - z = 7 \] \[ x - 3y + 2z = 1 \] \[ x + 4y + \delta z = k \] has infinitely many solutions, then \( \delta + k \) is:

• A. \( -3 \)
• B. \( 3 \)
• C. \( 6 \)
• D. \( 9 \)

Hint:

For infinitely many solutions, the determinant of the coefficient matrix and all augmented determinants must be zero.