Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Find $\text{adj } A$ for $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$

Options:

$\begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}$

$\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}$

$\begin{bmatrix} -4 & 3 \\ 1 & -2 \end{bmatrix}$

$\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$

Correct Answer:

$\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}$

Explanation:

The correct answer is Option (2) → $\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}$ ##

We have $A_{11} = 4, A_{12} = -1, A_{21} = -3, A_{22} = 2$

Hence

$\text{adj } A = \begin{bmatrix} A_{11} & A_{21} \\ A_{12} & A_{22} \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}$