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NDA Math Determinants

Question : 17 of 68

Marks: +1, -0

Let

A=\begin{vmatrix} p & q \\ r & s \end{vmatrix}

p, q, r

s

Solution: 👈: Video Solution

Concept:

Suppose A is a square matrix of 2 rows and 2 columns

A=\begin{bmatrix} a & b \\ c & d \end{bmatrix}

The determinant is;

\left|A\right|=\left[ad-bc\right]

Calculation:

A=\begin{vmatrix} p & q \\ r & s \end{vmatrix}

p, q, r

and

s

are any four different prime numbers less than 20 .

Here we have to find the maximum value of the determinant so we have to take maximum value for

p

and

All prime numbers less than

20=2,3,5,7,11,13,17,19

So,

p=17, q=2, r=3

and

s=19

A=\begin{vmatrix} 17 & 2 \\ 3 & 19 \end{vmatrix}

\left|A\right|=\left[17 \times 19-2 \times 3\right]

=323-6

=317

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