Question

Find the value of X if A=
2 3 4
-4 x -8
5 6 7
is a singular Matrix
​

Answer 1

Answer:

X = -6

Step-by-step explanation:

∵ the matrix is a single matrix only if its determinant = 0

∵ the determinant = 0 if any 2 columns or  any 2 rows  have a constant ratio between them

∵ - 4 = -2 x 2      

∵ - 8 = -2 x 4

∴ the 2nd column = - 2 x 1st column

$\left[\begin{array}{ccc}2&3&4\\-4&X&-8\\5&6&7\end{array}\right]$

∴ X = - 2 x 3

∴ X = - 6

∵

  $\left[\begin{array}{ccc}2&3&4\\-4&-6&-8\\5&6&7\end{array}\right]$  = 2 ( (-6x7) - (-8x6) ) - 3 ( (-4x7) - (-8x5) ) +4( (-4x6) -(-6x5) )

∴

 $\left[\begin{array}{ccc}2&3&4\\-4&-6&-8\\5&6&7\end{array}\right]$ = 0

∴ A is a single matrix