Question

If `[(1, 0, -1),(0, 2, 1),(1, -2, 0)] [(x),(y),(z)] = [(1),(2),(3)]`, then the values of x, y, z respectively are ______.

Options

• 2, 0, 3

• 3, 0, –2

• 3, 0, 2

• –2, 0, 3

Answer 1

If `[(1, 0, -1),(0, 2, 1),(1, -2, 0)] [(x),(y),(z)] = [(1),(2),(3)]`, then the values of x, y, z respectively are 3, 0, 2.

`[(1, 0, -1),(0, 2, 1),(1, -2, 0)] [(x),(y),(z)] = [(1),(2),(3)]`

∴ x –  z = 1   ......(i)

2y + z = 2 .......(ii)

x – 2y = 3  ......(iii)

Equations (i), (ii) and (iii) are satisfied by option 3, 0, 2.