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NDA Math Determinants

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Question : 22 of 68

Marks: +1, -0

Let

A=\begin{bmatrix} x+y & y \\ 2x & x-y \end{bmatrix}

B=\begin{bmatrix} 2 \\ -1 \end{bmatrix}

C=\begin{bmatrix} 3 \\ 2 \end{bmatrix}

A B = C,

then what is the value of the determinant of the matrix

A ?

-10
-14
-24
-34

Solution: 👈: Video Solution

AB=\begin{bmatrix} x+y & y \\ 2x & x-y \end{bmatrix}\begin{bmatrix} 2 \\ -1 \end{bmatrix}

=\begin{bmatrix} 2(x+y)-y \\ 4x-x+y \end{bmatrix}

=\begin{bmatrix} 2x+y \\ 3x+y \end{bmatrix}

As

AB = C

\therefore \begin{bmatrix} 2x+y \\ 3x+y \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \end{bmatrix}

2 x+y=3

....(i)

and

3 x+y=2

....(ii)

From equation (i) and (ii), we get

x=-1, y=5

\therefore A=\begin{bmatrix} -1+5 & 5 \\ -2 & -1-5 \end{bmatrix}

=\begin{bmatrix} 4 & 5 \\ -2 & -6 \end{bmatrix}

=4(-6)-5(-2)=-14

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