GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/01

Question 01 (Textile Technology & Fibre Science)

Let $A= \begin{bmatrix} a & b\\ 2 & -b \end{bmatrix}$ and $X= \begin{pmatrix} -1\\ 1 \end{pmatrix}$ . If $AX=\begin{pmatrix} -3\\ 1 \end{pmatrix}$ , then $\left | A \right |$ is equal to

(A)	2
(B)	-2
(C)	-6
(D)	6

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$A= \begin{bmatrix} a & b\\ 2 & -b \end{bmatrix}$ and $X= \begin{pmatrix} -1\\ 1 \end{pmatrix}$
$AX=\begin{bmatrix} a & b\\ 2 & -b \end{bmatrix} \times \begin{pmatrix} -1\\ 1 \end{pmatrix}$
$AX=\begin{bmatrix} -a+b\\ -2-b \end{bmatrix}=\begin{pmatrix} -3\\ 1 \end{pmatrix}$
So, -a+b=-3 and -2-b=1
Solve both equations-
a=0 and b=-3
Now, $A=\begin{bmatrix} 0 & -3\\ 2 & 3 \end{bmatrix}$
$\left | A \right |=0 \times 3+2 \times -3$
$\left | A \right |=6$ (Ans)

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