Question

16. For what value of x , A=

[2(x+1) 2x
x x - 2 ]
is a singular matrix​

Answer 1

Answer:

x= 0,2

Step-by-step explanation:

A singular matrix has det(A)=0   {det = Determinant}

here, taking your elements row-wise:

2(x+1)*2x - (x*(x-2))=0

4x^2 +4x= x^2-2x

3x^2-6x=0

x= 0,2

Answer 2

Answer:

$x=-2$

Step-by-step explanation:

Given a matrix, A= $\left[\begin{array}{ccc}2(x+1)&2x\\x&x-2\end{array}\right]$  

The question is, for what of x is the matrix a singular matrix?

What is a singular matrix?

• If the determinant of a matrix is 0, then that matrix is said to be a singular matrix.
• In this problem, we are expected to find the value of x where the matrix is singular.

To do that, let us find the determinant of the matrix A,

 

           $det\left[\begin{array}{ccc}2(x+1)&2x\\x&x-2\end{array}\right]$  $= 2(x+1)(x-1)-2x^{2}$

                                                $=2x^{2}-4x+2x-4-2x^{2}\\\\=-4x+2x-4\\\\=-2x-4$

Since for a singular matrix,  = 0

$det(A) = -2x-4=0$

                    $2x=-4$

                      $x=-2$

∴ The value of $x=-2$

Cross verification: $det\left[\begin{array}{ccc}2(x+1)&2x\\x&x-2\end{array}\right] = det\left[\begin{array}{ccc}2(-2+1)&2(-2)\\-2&-2-2\end{array}\right]$

                                                                     $=det\left[\begin{array}{ccc}-2&-4\\-2&-4\end{array}\right]$

                                                                     = -8-(-8)

                                                                     = -8+8 = 0

That is det(A) = |A| = 0 at $x=-2$.

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