Question

Find values of x , if (i) 2 4 5 1 = 2 x 4 6 x (ii) 2 3 4 5 = x 3 2 x 5

Answer 1

Take matrix,

[ 2 4 5 1 ]

Determinant of the given matrix is,

| 2 4 5 1 | =2×1−4×5 =−18 (1)

Now, determinant of the right hand side matrix is,

| 2x 4 6 x | =2x×x−4×6 =2 x 2 −24 (2)

As per the given question, equation (1) is equal to equation (2).

So,

2 x 2 −24=−18 2 x 2 =−18+24 x 2 =3 x=± 3

Thus, the value of x is ± 3 .