Question

Let matrix X = [x_ij] is given by X = `[(1, -1, 2),(3, 4, -5),(2, -1, 3)]`. Then the matrix Y = [m_ij], where m_ij = Minor of x_ij, is ______.

Options

• `[(7, -5, -3),(19, 1, -11),(-11, 1, 7)]`

• `[(7, -19, 11),(5, -1, -1),(3, 11, 7)]`

• `[(7, 19, -11),(-3, 11, 7),(-2, -1, -1)]`

• `[(7, 19, -11),(-1, -1, 1),(-3, -11, 7)]`

Answer 1

Let matrix X = [x_ij] is given by X = `[(1, -1, 2),(3, 4, -5),(2, -1, 3)]`. Then the matrix Y = [m_ij], where m_ij = Minor of x_ij, is `underlinebb([(7, 19, -11),(-1, -1, 1),(-3, -11, 7)])`.

Explanation:

`m_11 = |(4, -5),(-1, 3)| = 12 - 5 = 7`

`m_12 = |(3, -5),(2, 3)| = 9 + 10 = 19`

`m_13 = |(3, 4),(2, -1)| = -3 - 8 = -11`

`m_21 = |(-1, 2),(-1, 3)| = -3 + 2 = -1`

`m_22 = |(1, 2),(2, 3)| = 3 - 4 = -1`

`m_23 = |(1, -1),(2, -1)| = -1 + 2 = 1`

`m_31 = |(-1, 2),(4, -5)| = 5 - 8 = -3`

`m_32 = |(1, 2),(3, -5)| = -5 - 6 = -11`

`m_33 = |(1, -1),(3, 4)| = 4 + 3 = 7`

∴ `Y = [(7, 19, -11),(-1, -1, 1),(-3, -11, 7)]`