Question

what is x,(1 4 2 x) is singular matrix
a)5
b)6
c)7
d)8​

Answer 1

Given Matrix,

$\sf A = \left[\begin{array}{cc}1&4\\2&\sf x\end{array}\right]$

The above matrix is singular, in other words, det(A) = 0.

For a matrix of the order 2 × 2,

$\sf det(A) = a_{11}a_{22} - a_{12}a_{21}$

Therefore,

$\longrightarrow \sf det(A) = (1)(x) - (2)(4) \\ \\ \longrightarrow \sf 0 = x - 8 \\ \\ \longrightarrow \boxed{ \boxed{ \sf x = 8}}$

For x = 8, the above matrix is singular.

Option (D) is correct.

NOTE

• A matrix is said to be singular if det(A) = 0.
• A matrix is said to be non singular if det(A) ≠ 0.
• A matrix is symmetric if A = A', where A' is the transpose of A.
• A matrix is skew symmetric if A = -A'.
• A matrix is hermatian if A = Aⁿ.
• A matrix is skew hermatian if A = - Aⁿ.