To evaluate the determinant of the given matrix [tex]\( A = \left[\begin{array}{rr} -5 & 1 \\ 1 & 4 \end{array}\right] \)[/tex], we use the general formula for the determinant of a 2x2 matrix:
[tex]\[ \text{det}(A) = ad - bc \][/tex]
Where the matrix [tex]\( A \)[/tex] is given by:
[tex]\[ A = \left[\begin{array}{cc} a & b \\ c & d \end{array}\right] \][/tex]
In our case:
[tex]\[ A = \left[\begin{array}{rr} -5 & 1 \\ 1 & 4 \end{array}\right] \][/tex]
Here, [tex]\( a = -5 \)[/tex], [tex]\( b = 1 \)[/tex], [tex]\( c = 1 \)[/tex], and [tex]\( d = 4 \)[/tex].
Substituting these values into the determinant formula, we get:
[tex]\[ \text{det}(A) = (-5)(4) - (1)(1) \][/tex]
[tex]\[ \text{det}(A) = -20 - 1 \][/tex]
[tex]\[ \text{det}(A) = -21 \][/tex]
Thus, the determinant of the matrix is:
[tex]\[ \boxed{-21} \][/tex]
Therefore, the correct answer is:
D. -21
