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What is the determinant of matrix [tex]\( B \)[/tex]?
[tex]\[ B = \begin{pmatrix} 2 & 6 \\ -1 & 5 \end{pmatrix} \][/tex]

A. 16
B. -16
C. -4
D. 9
E. 4


Sagot :

To find the determinant of the matrix [tex]\( B = \begin{pmatrix} 2 & 6 \\ -1 & 5 \end{pmatrix} \)[/tex], we use the formula for the determinant of a [tex]\( 2 \times 2 \)[/tex] matrix.

Given a matrix [tex]\( B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \)[/tex], the determinant is calculated as:

[tex]\[ \text{det}(B) = ad - bc \][/tex]

For the given matrix [tex]\( B \)[/tex]:

[tex]\[ a = 2, \quad b = 6, \quad c = -1, \quad d = 5 \][/tex]

Substituting these values into the determinant formula:

[tex]\[ \text{det}(B) = (2 \cdot 5) - (6 \cdot -1) \][/tex]

[tex]\[ \text{det}(B) = 10 - (-6) \][/tex]

[tex]\[ \text{det}(B) = 10 + 6 \][/tex]

[tex]\[ \text{det}(B) = 16 \][/tex]

Thus, the determinant of the matrix [tex]\( B \)[/tex] is 16. Therefore, the correct answer is:

[tex]\[ \boxed{16} \][/tex]
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