The value of x, for which the matrix A = [(e^x - 2,e^7 + x),(e^2 + x,e^2x + 3)] is singular is … (a) 9 (b) 8 (c) 7

Question

The value of x, for which the matrix A = \(\begin{bmatrix}e^{x - 2} &e^{7 + x} \\[0.3em]e^{2 + x}&e^{2x + 3}\end{bmatrix}\) is singular is …

(a) 9

(b) 8 

(c) 7 

(d) 6

Answer 1

(b) 8

Given A is a singular matrix ⇒ |A| = 0

(i.e.) \(\begin{bmatrix}e^{x - 2} &e^{7 + x} \\[0.3em]e^{2 + x}&e^{2x + 3}\end{bmatrix}\)= 0

⇒ e^{x - 2}.e^{2x + 3} – e^{2 + x}.e^{7 + x} = 0 

⇒ e^{3x + 1} – e^{9 + 2x} = 0 

⇒ e^{3x + 1} = e^{9 + 2x} 

⇒ 3x + 1 = 9 + 2x 

3x – 2x = 9 – 1 ⇒ x = 8