GATE Electrical 2024 | Question: 1

Question

 

​​​​Which one of the following matrices has an inverse?

• A. $\left[\begin{array}{ccc}1 & 4 & 8 \\ 0 & 4 & 2 \\ 0.5 & 2 & 4\end{array}\right]$
• B. $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 2 & 9\end{array}\right]$
• C. $\left[\begin{array}{lll}1 & 4 & 8 \\ 0 & 4 & 2 \\ 1 & 2 & 4\end{array}\right]$
• D. $\left[\begin{array}{ccc}1 & 4 & 8 \\ 0 & 4 & 2 \\ 3 & 12 & 24\end{array}\right]$

Answer 1

Inverse of a square matrix exists only if the matrix is non-singular(non-zero determinant).

Option 1: Incorrect(R1 and R3 are dependent so that  det = 0)

Option 2: Incorrect(R1 and R2 are dependent so that det = 0)

Option 3: Correct

Option 4: Incorrect(R1 and R3 are dependent so that det = 0)

Answer 2

Ans is 3.

For inverse, determinant of A should be non-zero..

 

Inverse of A = adjoint of A / determinant of A

Answer 3

The matrix which have inverse will have a determinent value .