The value of the variable b will be 8. Then the correct option is B.
What is determinant?
The determinant in math is a scalar quantity that is a result of the rows and columns of a matrix form.
If the determinant of this matrix is 24.
The matrix is given below.
[tex]\begin{bmatrix}-5 & 4 & 1 \\5 & -7 & -4 \\-6 & b & 6 \\\end{bmatrix}[/tex]
R₁ ⇒ R₁ + R₂
[tex]\begin{bmatrix}0 & -3 & -3 \\5 & -7 & -4 \\-6 & b & 6 \\\end{bmatrix}[/tex]
C₂ ⇒ C₂ – C₃
[tex]\begin{bmatrix}0 & 0 & -3 \\5 & -3 & -4 \\-6 & b-6 & 6 \\\end{bmatrix}[/tex]
Then the value of b will be
–3[5(b – 6) – (–3)(–6)] = 24
(5b – 30 – 18) = –8
5b = 40
b = 8
Then the correct option is B.
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