Question

The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.

विकल्प

• `[(4, 8, 3),(2, 1,6),(0, 2, 1)]`

• `[(1, -1, 0),(-2, 3, -4),(-2, 3, -3)]`

• `[(11, 9, 3),(1, 2, 8),(6, 9, 1)]`

• `[(1, -2, 1),(-1, 3, 3),(-2, 3, -3)]`

Answer 1

The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is `bbunderline([(1, -1, 0),(-2, 3, -4),(-2, 3, -3)])`.

Explanation:

`M_11 = |(-3, 4), (-1, 1) = -3 + 4 = 1|`

`M_12 = |(2, 4), (0, 1)| = 2 + 0 = 2`

`M_13 = |(2, -3), (0, -1)| = -2 + 0 = -2`

`M_21 = |(-3, -1), (-1, 1)| = -3 + 4 = 1`

`M_22 = |(3, 4), (0, 1)| = 3 - 0 = 3`

`M_23 = |(3, -3), (0, -1)| = -3 + 0 = 3`

`M_31 = |(-3, 4), (-3, 4)| = 12 - 8 = 4`

`M_32 = |(3, 4), (2, 4)| = 12 - 8 = 4`

`M_33 = |(3, -3), (2, -3)| = -9 + 6 = 3`

A₁₁ = −1

A₁₂ = −2

A₁₃ = −2

A₂₁ = −1

A₂₂ = 3

A₂₃ = 3

A₃₁ = 0

A₃₂ = −4

A₃₃ = −3

[Cofactor A] = `[(-1, -2, -2), (-1, 3, 3), (0, -4, -3)]`

Adj (A) = (Cof A)^T

`[(-1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`