Question

[tex] If\left|\begin{array}{ccc}1&2&5\\1 &x&5\\3&-1&2\end{array}\right|

= 0 are......,Select Proper option from the given options.

(a) 2

(b) -2

(c) 5

(d) -5
[/tex]

Answer 1

Dear Student,

Answer: x = 2 ( option a is correct)

Solution:

$If\left|\begin{array}{ccc}1&2&5\\1 &x&5\\3&-1&2\end{array}\right|$ = 0

Now Apply some Row elementary operations,to simplify the determinant

Apply R1 -> R1 -R2

$If\left|\begin{array}{ccc}0&2-x&0\\1 &x&5\\3&-1&2\end{array}\right|$ = 0

Now expand the determinant for Row 1 (R1)

$0(2x + 5) - (2 - x)(2 - 15) + 0( - 1 - 3x) = 0 \\ \\ - (2 - x)( - 13) = 0 \\ \\ 2 - x = 0 \\ x = 2$
So x = 2, for the given Determinant to be zero.

Hope it helps you.